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205980913 Ibps Po 2013 Quantitative Aptitude eBook 1
Citation preview
5/21/2018 205980913 Ibps Po 2013 Quantitative Aptitude eBook 1
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5/21/2018 205980913 Ibps Po 2013 Quantitative Aptitude eBook 1
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2 IBPS BANK PO EXAM 2013 : Quantitative Aptitude
Table of Contents
PREFACE ............................................................................................................................................. 6
IMPORTANT CHAPTER GUIDELINES ........................ ........................... ......................... ............... 7
CHAPTER: SIMPLIFICATION & APPROXIMAITON ................................................................... 8
Solved Examples (Simplification & Approximation) ............................................................................................. 12
Practice Set-1 (Simplification & Approximation) .................................................................................................. 22
Practice Set-2 (Simplification & Approximaiton) .................................................................................................. 25
Simplification & Approximaiton Averages Practice Set-1 (Answers) .................................................................... 27
Simplification & Approximaiton Averages Practice Set-2 (Answers) .................................................................... 28
CHAPTER: NUMBER SERIES ....................... .......................... ......................... ........................... .... 29
Solved Examples (Number Series) ........................................................................................................................ 33
Practice Set (Number Series)................................................................................................................................ 38
Number Series Practice Set (Answers) ................................................................................................................. 41
CHAPTER: NUMBER SYSTEM .......................... .......................... ......................... ......................... . 42
Solved Examples (Number System) ...................................................................................................................... 48
Practice Set-1 (Number System) .......................................................................................................................... 53
Practice Set-2 (Number System) .......................................................................................................................... 55
Number System Practice Set-1 (Answers) ............................................................................................................ 58
Number System Practice Set-2 (Answers) ............................................................................................................ 59
CHAPTER: RATIO, PROPORTION & ALLIGATION ........................................ ......................... . 60
Solved Examples (Ratio, Proportion & Alligation) ................................................................................................ 66
Practice Set-1 (Ratio, Proportion & Alligation) ..................................................................................................... 70
Practice Set-2 (Ratio, Proportion & Alligation) ..................................................................................................... 74
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3 IBPS BANK PO EXAM 2013 : Quantitative Aptitude
Ratio, Proportion & Alligation Practice Set-1 (Answers) ....................................................................................... 77
Ratio, Proportion & Alligation Practice Set-2 (Answers) ....................................................................................... 78
CHAPTER: AVERAGES ................................................................................................................... 79
Solved Examples (Averages) ................................................................................................................................ 80
Practice Set (Averages) ........................................................................................................................................ 86
Averages Practice Set (Answers) .......................................................................................................................... 90
CHAPTER: PERCENTAGES, PARTNERSHIP AND SHARE .......................................... ............. 91
Solved Examples (Percentages, Partnership and Share) ....................................................................................... 95
Practice Set-1 (Percentages, Partnership and Share) .......................................................................................... 101
Practice Set-2 (Percentages, Partnership and Share) .......................................................................................... 104
Percentages, Partnership and Share Practice Set-1 (Answers) ........................................................................... 106
Percentages, Partnership and Share Practice Set-2 (Answers) ........................................................................... 107
CHAPTER: PROFIT & LOSS ........................................................................................................ 108
Solved Examples (Profit & Loss) ......................................................................................................................... 112
Practice Set (Profit & Loss) ................................................................................................................................. 117
Profit & Loss Practice Set (Answers) .................................................................................................................. 121
CHAPTER: SIMPLE INTEREST & COMPOUND INTEREST ................................ .................. 122
Solved Examples (Simple Interest & Compound Interest) .................................................................................. 126
Practice Set (Simple Interest & Compound Interest) .......................................................................................... 132
Simple Interest & Compound Interest Practice Set (Answers) ............................................................................ 136
CHAPTER: TIME AND WORK .................................................................................................... 137
Solved Examples (Time and Work) ..................................................................................................................... 140
Practice Set (Time and Work)............................................................................................................................. 146
Averages Practice Set (Time and Work) ............................................................................................................. 151
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4 IBPS BANK PO EXAM 2013 : Quantitative Aptitude
CHAPTER: SPEED DISTANCE & TIME ..................................................................................... 152
Solved Examples (Speed Distance & Time)......................................................................................................... 156
Practice Set (Speed Distance & Time) ................................................................................................................ 162
Speed Distance & Time Practice Set (Answers) .................................................................................................. 166
CHAPTER: MENSURATION ........................................................................................................ 167
Solved Examples (Mensuration) ........................................................................................................................ 174
Practice Set (Mensuration) ................................................................................................................................ 178
Mensuration Practice Set (Answers) .................................................................................................................. 181
CHAPTER: PERMUTATIONS, COMBINATIONS & PROBABILITY ..................................... 182
Solved Examples (Permutations, Combinations & Probability) .......................................................................... 188
Practice Set-1 (Permutations, Combinations & Probability) ............................................................................... 195
Practice Set-2 (Permutations, Combinations & Probability) ............................................................................... 197
Permutations, Combinations & Probability Practice Set-1 (Answers) ................................................................. 199
Permutations, Combinations & Probability Practice Set-2 (Answers) ................................................................. 200
CHAPTER: DATA INTERPRETATION ...................................................................................... 201
CHAPTER: DATA INTERPRETATION-TABLE CHART ......................................................... 204
Solved Examples (Data Interpretation-Table Chart) ........................................................................................... 206
Practice Set (Data Interpretation-Table Chart) ................................................................................................... 213
Data Interpretation-Table Chart Practice Set (Answers) .................................................................................... 221
CHAPTER: DATA INTERPRETATION-LINE GRAPHS ........................ ......................... .......... 222
Solved Examples (Data Interpretation-Line Graphs) .......................................................................................... 225
Practice Set (Data Interpretation-Line Graphs) .................................................................................................. 229
Data Interpretation-Line Graphs Practice Set (Answers) .................................................................................... 233
CHAPTER: DATA INTERPRETATION-BAR GRAPHS ......................... ......................... .......... 234
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5 IBPS BANK PO EXAM 2013 : Quantitative Aptitude
Solved Examples (Data Interpretation-Bar Graphs)............................................................................................ 237
Practice Set (Data Interpretation-Bar Graphs) ................................................................................................... 243
Data Interpretation-Bar Graphs Practice Set (Answers) ..................................................................................... 247
CHAPTER: DATA INTERPRETATION-PIE DIAGRAM .......................................................... 248
Solved Examples (Data Interpretation-Pie Diagram) .......................................................................................... 250
Practice Set (Data Interpretation-Pie Diagram) .................................................................................................. 256
Data Interpretation- Pie Diagram Practice Set (Answers) ................................................................................... 262
CHAPTER: DATA INTERPRETATION-CASE LETS ................................................................ 263
Solved Examples (Data Interpretation-Caselets) ................................................................................................ 266
PracticeSet-(Data Interpretation- Caselets)........................................................................................................ 270
Data Interpretation-Caselets Practice Set (Answers).......................................................................................... 274
Solved Examples (Data Interpretation-Miscellaneous) ...................................................................................... 275
Practice Set (Data Interpretation-Miscellaneous) .............................................................................................. 285
Data Interpretation-Miscellaneous Practice Set (Answers) ................................................................................ 291
FEEDBACK ..................................................................................................................................... 292
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6 IBPS BANK PO EXAM 2013 : Quantitative Aptitude
Preface
Jagranjoshs IBPS PO Exam 2013: Quantitative Aptitude e-Book is a one-stop solution for aspirants who
endeavor to leave no stone unturned to score considerably in IBPS PO Written Examination 2013. The
eBook is highly useful for all officers level Banking exams - IBPS Specialist officers Exam and SBI PO
Exam.
IBPS PO Exam 2013: Quantitative Aptitude e-Book is prepared by Jagranjoshs team of subject matter
experts who worked up the best to come up with this all-inclusive preparation package for Quantitative
Aptitude section of Officers level Banking Exams. This eBook is a perfect blend of chapter-wise basic
concepts and questions regarding all the units included in the syllabus for Quantitative Aptitude Section
of Officers level Banking Exams. The chapter-wise compilation of this e-Book makes the concept of
Quantitative aptitudes easy to understand for students. It further includes previous year questions andmodel practice sets along with the importance factor of each and every chapter included out here.
Our IBPS PO Exam 2013: Quantitative Aptitude e-Book will let students to practice for the QA section
within the standard time limit set by the IBPS examination board. This will help them hone time
management skills.
The IBPS PO Exam 2013: Quantitative Aptitude e-Book includes:
Chapter wise Basic Concepts & Questions
IBPS PO Previous Year Questions
Chapter wise Model Practice Set
Important Chapter Guidelines
Jagranjoshs IBPS PO Exam 2013: Quantitative Aptitude e-Book is a one-stop solution edition to help
preparing for the QA Section of Officers level Banking Exams. All the chapters of this e-book are reader-
friendly and easy to understand. Just prepare with it to score more.
Our team at Jagranjosh.com wishes all the very best to the aspirants of Banking Exams.
All the Best!
Copyright Jagranjosh.com
All rights reserved. No part or the whole of this eBook may be copied, reproduced, stored in retrieval system or transmitted
and/or cited anywhere in any form or by any means (electronic, mechanical, photocopying, recording or otherwise), without
the written permission of the copyright owner. If any misconduct comes in knowledge or brought in notice, strict action will betaken.
Disclaimer
Readers are requested to verify/cross-check up to their satisfaction themselves about the advertisements, advertorials, and
external contents. If any miss-happening, ill result, mass depletion or any similar incident occurs due to any information cited or
referenced in this e-book, Editor, Director/s, employees of Jagranjosh.com cant be held liable/responsible in any matter
whatsoever. No responsibilities lie as well in case of the advertisements, advertorials, and external contents.
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7 IBPS BANK PO EXAM 2013 : Quantitative Aptitude
Important Chapter Guidelines
Important Chapter Guidelines for IBPS PO 2013 : Quantitative Aptitude
Chapter Importance
Number System Very Important
Number Series Very Important
Percentage Partnership and Share Very Important
Simplification and Approximation Very Important
Average Important
Ratio ,Proportion & Alligation Important
Time & Work Important
Profit, Loss & Discount Very Important
Simple Interest and Compound Interest Important
Time, Distance and Speed Important
Permutation and Combination & Probability Very Important
Data Interpretation-Table Charts Very Important
Data Interpretation-Bar Graph Very Important
Data Interpretation-Line Graph Very Important
Data Interpretation-Pie Charts Very Important
Data Interpretation-Caselets Very Important
Data Interpretation-Miscelleneous Graphs Very Important
Mensuration Important
Note : Prepared on the basis of questions asked in previous year papers
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8 IBPS BANK PO EXAM 2013 : Quantitative Aptitude
Chapter: Simplification & ApproximaitonSome Important Concepts
BODMAS Rule: This BODMAS Rule shows the correct sequence of all the operations that are
to be executed to find out the value of a given expression. In this rule B Stands for Bracket,
O stands for of, D for Division, M for Multiplication, A for Addition and S for
Subtraction.
Therefore, the correct order to simplify an expression is:
(a)
( )(b){}
(c) []
(d)
of
(e)Division
(f) Multiplication
(g) Addition
(h)Subtraction
Modulus of a Real Number:If the real number is r, then
| r | = .
Example: What will be the value of x in the following equation?
5 + + x +2 = 9 .
Solution:Simplifying the above equation
x = 9 - 5 - 2 x = - - -
x =
x = = 1 .
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9 IBPS BANK PO EXAM 2013 : Quantitative Aptitude
Example: If = , then find the value of .
Solution:Given expression: =
(x/y =3/2)
.
Example: Arjun spends of his salary on house rent, of his salary on food and of his salary
on conveyance. If he has Rs.2400 left with him, then find his expenditure on conveyance.
Solution:Suppose Arjuns monthly salary is Rs. x
Then, remaining part of his salary = x- ( + + ) x = x( ) x = = .
Now, = 2400 x =Rs. 4500.
Expenditure on Conveyance = Rs.( 4500 ) = Rs.450.
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10 IBPS BANK PO EXAM 2013 : Quantitative Aptitude
Approximation
In these types of questions there is no need to find out the exact values. The candidate is
required to calculate the approximate value in the following manner:
Step I:Round off the numbers given in the question.
Step II:Simplify the value
Step III:Round off the final simplified value
Rounding off numbers:
Rounding off the numbers given in the question can be done in the following manner:
(a)
Rounding off to the nearest 10:
Example:Rounded off value of 56 is 60, because the digit at unit place is greater than 5,
therefore, we will add 1 to the digit at tens place and replace the units digit by 0.
Example:Rounded off value of 54 is 50, because the digit at unit place is less than 5,
therefore, the value at tens place will remains the same and units digit will be replaced
by 0.
Example:Rounded off value of 35 is 40, because the digit at unit place is equal to 5,
therefore, we will add 1 to the digit at tens place and replace the units digit by 0.
(b)
Rounding off to the nearest 100:
Example:Rounded off value of 386 is 400, because the digit at tens place is greater than
5, therefore, we will add 1 to the digit at hundreds place and replace the digit at unit
and tens places by 00.
Example:Rounded off value of 741 is 700, because the digit at tens place is less than 5,
therefore, the value at hundreds place will remains the same. Unit and tens digit will be
replaced by 00.
(c)
Rounding off to the nearest 1000
Example: Rounded off value of 1963 is 2000, because the digit at hundreds place is
greater than 5, therefore, we will add 1 to the digit at thousand place and replace the
ones, tens and hundreds by 000.
Although the numbers can be rounded off by the above procedures but it depends on the other
numbers involved in the simplification.
Rounding off a number to a decimal place:
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11 IBPS BANK PO EXAM 2013 : Quantitative Aptitude
The candidate is required to follow the following steps to round off a number to the nth
decimal place:
Step I:check the digit immediately, next right to the nth place.
Step II:Add 1 to the digit in the nth place, if the next right digit is 5 or more, otherwise the digit
will remains the same.
Step III:Remove all the digits in places to the right of the nth place.
Example:Rounded off value of 4.693 to the second place is 4.69, because next right digit to the
second place is 3, therefore, the value will remain the same and the digit in place to the right of
the second place will be removed.
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12 IBPS BANK PO EXAM 2013 : Quantitative Aptitude
Solved Examples (Simplification & Approximation)
Directions (1-5) What will come in place of the question mark (?) in the following question?
(IBPS PO/MT Exam 2012)
1. 4003 77 - 21015=? 116
(1) 2477
(2) 2478
(3) 2467
(4) 2476
(5) None of these
Solution:? 116 = 4003 7721015
or, ? 116 = 30823121015 = 287216
or, ? 116 = 287216
? = = 2476
Ans: (4)
2.
(1) 143
(2)
(3) 134
(4)
(5) None of these
Solution:
=- 361
= - 361
= 504 -361 = 143
Ans: (1)
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13 IBPS BANK PO EXAM 2013 : Quantitative Aptitude
3. (444440) + (64525) + (399126) =?
(1) 280.4
(2) 290.4(3) 295.4
(4) 285.4
(5) None of these
Solution:(444440) + (64525) + (399126)
= + +
= 111.1 + 25.8 + 153.5 = 290.4
Ans: (2)
4. - (83)2
= (?)2+ (37)
2
(1) 37
(2) 33
(3) 34
(4) 38
(5) None of these
Solution:(?)2
+ (37)2= - (83)
2
or, (?)2+ (37)
2= 18251 - (83)
2
or, (?)2+ 1369 = 9282-6889 =2393
or, (?)2= 2393 - 1369 = 1024
?= = 32
Ans: (5)
5.5 4 11 + 2 =?
(1) 303.75
(2) 305.75
(3)
(4)
(5) None of these
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14 IBPS BANK PO EXAM 2013 : Quantitative Aptitude
Solution: ?= 5 4 11 + 2
= +
= +
= 101 3 + = 303 + =
= = 305.75
Ans: (2)
Direction (6-10): What approximate value should come in place of the question mark (?) in
the following question? (Note: You are not excepted to calculate the exact value.)
(IBPS PO/MT Exam 2012)
6. 8787 343 =?
(1) 250
(2) 140
(3) 180
(4) 100
(5) 280
Solution:? = 8787 343
= 25.61 7.07 = 181.09
Ans: (3)
7. (3038) = (?)2
(1) 48(2) 38
(3) 28
(4) 18
(5) 58
Solution: (3038) = (?)2
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15 IBPS BANK PO EXAM 2013 : Quantitative Aptitude
or, 38 37.8 = (?)2 (37.8 ~ 38)
or, 38 38 = (?)2
Ans: (2)
8. of 4011.33 + of 3411.22 =?
(1) 4810
(2) 4980
(3) 4890
(4) 4930
(5) 4850
Solution:? = 4011.33 + 3411.22
= +
= 2507.08 + 2387.854 = 2507 + 2387
= 4894
Ans: (3)
9. 23% of 6783 + 57% of 8431=?
(1) 6460
(2) 6420
(3) 6320
(4) 6630
(5) 6360
Solution:?= 23% of 6783 + 57% of 8431
6783 + 8431
= 23
= 1560.09 + 4805.67 = 6365.76
Ans: (5)
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16 IBPS BANK PO EXAM 2013 : Quantitative Aptitude
10. 335.01 244.9955=?
(1) 1490
(2) 1550(3) 1420
(4) 1590
(5) 1400
Solution:? = 335.01 244.99 55
= 335 245 55
= 335 = = 1422.27 1490
Ans: (1)
Directions (Q.11-15): What will come in place of the question mark (?) in the following
questions?
(IBPS PO/MT Exam 2011)
11. 3463 295 - 18611 =? + 5883
(1) 997091
(2) 997071
(3) 997090
(4) 999070
(5) None of these
Solution: 3463 x 295 -18611 =? + 5883
? = 1021585 - 18611 - 5883 = 997091
Ans: (1)
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17 IBPS BANK PO EXAM 2013 : Quantitative Aptitude
12. (23.1)2+ (48.6)
2- (39.8)
2=? + 1147.69
(1) (13.6)2
(2)
(3) 163.84
(4) 12.8
(5) None of these
Solution:533.61 + 2361.96 - 1584.04 =? + 1147.69
or, ? = 1311.53 - 1147.69 = 163.84
Ans: (3)
13. + = ?
1)
2) 0.75
3) 1
4) None of these
Solution: + = = = =
Ans: (4)
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18 IBPS BANK PO EXAM 2013 : Quantitative Aptitude
14. [(3 + ) X (8 + 7 )]- 98 =?
(1) 2
(2) 8
(3) 382
(4) 386
(5) None of these
Solution: [ (3 +1) (8 + 7) ]- 98
= [4 15 ] - 98
= [60 8] - 98 = 480 - 98 = 382
Ans: (3)
15. - (54)2= + (74)
2
(1) 3844
(2) 3721
(3) 3481
(4) 3638
(5) None of these
Solution: - (54)2 - (74)2=
or , = - 2916 - 5476
= 8453 - 2916 - 5476 = 61
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19 IBPS BANK PO EXAM 2013 : Quantitative Aptitude
or , ? = (61)2= 3721
Ans: (2)
Directions ( 16-20): What approximate value should come in place of question mark (?) in the
following questions?
(Note: You are not expected to calculate the exact value](IBPS PO/MT Exam 2011)
16. 39.897% of 4331 + 58.779% of 5003 =?
(1) 4300
(2) 4500
(3) 4700
(4) 4900
(5) 5100
Solution: 40 + 59 = 1732 + 2950 = 4682 4700
Ans: (3)
17. 43931.03 / 2111.02 x 401.04 =?
1) 8800
2) 7600
3) 7400
4) 9000
5) 8300
Solution:43931 2111 401 =?
or, ? = 44000 400
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20 IBPS BANK PO EXAM 2013 : Quantitative Aptitude
or, ? = 400 = 8800
Ans: (5)
18. 34.993 =?
1) 3000
2) 2800
3) 2500
4) 3300
5) 2600
Solution: 34.993 = 80 x 35 = 2800
Ans: (2)
19. +349 =? 21.003
1) 7600
2) 7650
3) 7860
4) 7560
5) 7680
Solution: 17 + 349 =? 21
or, 366 21 = ?
or, ? = 7686 7680.
Ans: (5)
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21 IBPS BANK PO EXAM 2013 : Quantitative Aptitude
20. 59.88 12.21 6.35 =?
1) 10
2) 50
3) 30
4) 70
5) 90
Solution:60 12 6 = 30
Ans: (3)
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Practice Set-1 (Simplification & Approximation)
Directions (Q. 1-5): What will come in place
of question mark (?) in the following
questions?(IBPS RRB Grade A Officer Exam
2012)
1.
(1)
(2)
2
(3)16
(4)8
(5)None of these
2. 55% of
(1)126.5
(2)126.6
(3)
124.6(4)125.4
(5)None of these
3.
(1)
(2)
(3)(4)18
(5)32
4.
(1)81
(2)64
(3)8
(4)7
(5)9
5.
(1)6
(2)
2(3)4
(4)0
(5)None of these
Directions (Q. 6-10). What approximate
value will come in place of question mark
(?) in the following questions? (You are not
expected to calculate the exact value.)
6. 68% of 1288 + 26% of 734215 =?
(1)620
(2)930
(3)540
(4)
850
(5)710
7.
(1)670
(2)530
(3)
420
(4)780
(5)960
8. 6578 67 15 =? 6
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23 IBPS BANK PO EXAM 2013 : Quantitative Aptitude
(1)200
(2)250
(3)150
(4)
100(5)300
9.
(1)540
(2)760
(3)800
(4)1260
(5)1040
10.
(1)840
(2)910
(3)1320
(4)1120
(5)1550
Directions (Q.11 to 15): What will come in
place of question mark (?) in the following
questions? (RBI Grade B Officers Exam
2011)
11. [(3024 189)1/2 + (684 19)2] = (?)2 +
459
(1) -27
(2) -29
(3)31
(4)841
(5)1089
12. 4.4 times of 30% of 216 =?
(1)81.9
(2)83.7
(3)87.3
(4)89.1
(5)None of these
13. (0.0729 0.1)3 (0.081 10)
5 (0.3
3)
5
= (0.9
)? + 3
(1)1
(2)2
(3)4
(4)7
(5)None of these
14. of 5) = 149.8112
(1)(2)18
(3)324
(4)24
(5)None of these
15. (27)2 6 9 + (7)
3+ 71 = (?)
3431
(1)
11
(2) (13)3
(3)13
(4)
(11)
2
(5)None of these
Directions (Q. 16-20): What will come in
place of question mark (?) in the following
questions?(Corporation Bank PO Exam
2011)
16. 59071296 144 = ? 8
(1)726.75
(2)767.25
(3)
737.25
(4)676.75
(5)None of these
17.
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24 IBPS BANK PO EXAM 2013 : Quantitative Aptitude
(1)
(2)
(3)3
(4)9
(5) -3
18.
(1)11
(2)5
(3)7
(4)9
(5)
None of these
19.
(1)
(2)200
(3)
(4)100
(5)10
20.
(1)169
(2)13
(3)14
(4)196
(5)
None of these
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25 IBPS PO EXAM 2013 : Quantitative Aptitude
Practice Set-2 (Simplification & Approximaiton)
Directions (Q. 1-5): What approximate
value will come in place of question mark
(?) in the following questions?
(Corporation Bank PO Exam 2011)
(You are not expected to calculate the
exact value.)
1. 3237 31 15 = ? 17
(1)
90
(2)100
(3)110
(4)120
(5)80
2.
(1)1760
(2)1880
(3)
1950
(4)1720
(5)1650
3. (34.34)2+ (5.96)
2(23.09)
2=?
(1)510
(2)540
(3)620
(4)680
(5)650
4.
(1)200
(2)180
(3)120
(4)140
(5)160
5. 61% of 981150.17 = ?65% of 676
(1)760
(2)
780
(3)830
(4)860
(5)890
Directions-(Q. 6-10): What will come in
place of question-mark (?) in the following
questions?(Allahabad Bank Probationary
Officers Exam 2011)
6. of 30% of 3420 = (?)2x 2
(1) (81)2
(2)7
(3)9
(4)
81
(5)49
7. 1898 73 x 72 = (?)2x 13
(1) - 256
(2)256
(3)12
(4)144
(5) -16
8. =?
(1)42
(2)1024
(3)1764
(4) (1024)2
(5)32
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26 IBPS PO EXAM 2013 : Quantitative Aptitude
9. (081)2+ (0729)
3x (09)
2= (0.9)
?-3
(1)6
(2)
2(3)4
(4)0
(5)None of these
10. 65% of x 5 =? + 154
(1)56
(2)28
(3)35
(4)32
(5)
None of these
Directions-(Q. 11-15) What approximate
value will come in place of question-mark
(?) in the
following questions?(Allahabad Bank
Probationary Officers Exam 2011)
(You are not expected to calculate the
exact value.)
11. =? 8
(1)620
(2)670
(3)770
(4)750
(5)700
12. 89988% of 6999 + 50002% of 99999 -
170015 =?
(1)
990(2)900
(3)920
(4)960
(5)860
13. =?
(1)760
(2)800
(3)
690(4)870
(5)780
14. 6999 70005 x 94998 =? x 19999
(1)475
(2)420
(3)320
(4)540
(5)525
15. (4999)2(89)2(159)2=?
(1)2165
(2)2000
(3)1965
(4)1920
(5)1885
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Simplification & Approximaiton Averages Practice Set-1
(Answers)
1) 5
2) 1
3) 1
4) 4
5) 3
6) 4
7) 2
8) 2
9) 5
10) 3
11) 2
12) 4
13) 1
14) 5
15) 1
16) 3
17) 2
18) 4
19) 5
20) 2
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Simplification & Approximaiton Averages Practice Set-2
(Answers)
1) 1
2) 1
3) 5
4) 3
5) 5
6) 3
7) 3
8) 5
9) 4
10) 2
11) 2
12) 4
13) 4
14) 1
15) 1
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Chapter: Number SeriesIn Number Series, questions are asked on the basis of relation between numbers given in a
series. The questions asked can be divided into different types:
Type I:In this type of questions, a series of numbers is given with one number missing
represented by a question mark. Candidate has to select from the options choices to correct
option in place of the question mark. The given sequences of numbers will be such that each
number follows its predecessor in the same way, i.e., according to a particular pattern.
Candidates are required to find out the correct ways in which the sequence is formed and there
after find out the number to complete the series.
1. 30, 34, 43, 59, 84, 120,?
(1) 169
(2) 148
(3) 153
(4) 176
(5) None of these
Solution: (1)The given pattern is:
+22, 3
2, +4
2, + 6
2, +7
2
So, missing term is 169=120 +72
2. 40, 54, 82,?, 180,250
(1) 142
(2) 124
(3) 136
(4) 163
(5) None of these
Solution: (2)The pattern is: +14, + 28, + 42, + 52, + 70
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So, missing term is 82 + 42=124
Type II:Here, we are given a sequence of number. Whole sequence, except the odd number
follow a certain rule. You have to find that number which does not follow the rule.
1. 0, 1,3,8,18,35,264
(1) 62
(2) 35
(3) 18
(4) 8
(5) None of these
Solution: (1)The pattern is +(02+1), +(1
2+1), + (2
2+1) ,+ (3
2+1), + (4
2+1), + (5
2+1)
So, 62 is wrong and must be replaced by 35 + (52+1) = 62
2. 1, 9, 125, 49, 729, 121, 2147
(1) 2147
(2) 729
(3) 125
(4) 1
(5) None of these
Solution: (1)
Type III:In this type of questions, a number series is given. After the series is over, in the next
line, a number is followed by (A), (B), (C), (D) and (E). The candidates have to complete the
series starting with the number given following the sequence of the given series.
1. 2, 4, 9, 20, 43, 90
3 (A) (B) (C) (D) (E)
Which number will come in place of (D)?
(1) 58
(2) 99
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(3) 48
(4) 59
(5) None of these
Solution: (4)
Similarly,
Hence, the number 59 will come in place of D.
2. 3, 4, 10, 33, 136,
3 (A) (B) (C) (D) (E)
Which number will come in place of (E)?
(1) 1035
(2) 1165
(3) 1039
(4) 891
(5) None of these
Solution: (2)
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Similarly,
Hence, the number 1165 will come in place of E.
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Solved Examples (Number Series)
Directions: (1-5) In each of these questions a number series is given. In each series only one
number is wrong. Find out the wrong number.(IBPS CWE PO MT 2012)
1. 5531 5506 5425 5304 5135 4910 4621
(1) 5531
(2) 5425
(3) 4621
(4) 5135
(5) 5506
Solution:The number should be 5555 in place of 5531.
-72, -9
2, -11
2, -13
2, -15
2, -17
2...
Ans: (1)
2. 6 7 9 13 26 37 69
(1) 7(2) 26
(3) 69
(4) 37
(5) 9
Solution:The number should be 21 in place of 26.
+1, +2, +4, +8, +16, +32
Ans: (2)
3. 1 3 10 36 152 760 4632
(1) 3
(2) 36
(3) 4632
(4) 760
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(5) 152
Solution:The number should be 770 In place of 760.
1 +2, 2 +4, 3 +6, 4 + 8, 5 +10, 6 + 12, ...Ans: (4)
4. 4 3 9 34 96 219 435
(1) 4
(2) 9
(3) 34
(4) 435
(5) 219
Solution:The series is 02+ 4, 1
2+2, 3
2+0, 6
2-2, 10
2-4, 15
2- 6,21
2- 8...
Hence, 435 should be replaced with 433
Ans: (1)
5. 157.5 45 15 6 3 2 1
(1) 1
(2) 2
(3) 6
(4) 157.5(5) 45
Solution:The number should be 2 in place of 1.
3.5, 3, 2.5, 2, 1.5, 1, ...
Ans: (1)
Directions (6-10): In the following number series only one number is wrong.
Find out the wrong number.
6. 7 12 40 222 1742 17390 208608
(1) 7
(2) 12
(3) 40
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(4) 1742
(5) 208608
Solution: The pattern of number series is as follows:
7 2 - 2 = 12
12 4 - (2 + 6) = 48 - 8 = 40
40 6 - (8 + 10) = 240 - 18 = 222
222 8 - (18 + 14) = 1776 - 32 = 1744 1742
1744 10 - (32 + 18) = 17440 - 50 = 17390
Ans:(4)
7. 6 91 584 2935 11756 35277 70558
(1) 91
(2) 70558
(3) 584
(4) 2935
(5) 35277
Solution:The pattern of number series is as follows:
6 7 + 72= 42 + 49 = 91
91 6 + 62= 546 + 36 = 582 584
582 5+52=2910 + 25=2935
2935 4 + 42= 11740 + 16 = 11756
11756 x 3 + 32= 35268 + 9 = 35277
Ans: (3)
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8. 9050 5675 3478 2147 1418 1077 950
(1) 3478
(2) 1418
(3) 5675
(4) 2147
(5) 1077
Solution:The pattern of number series is as follows:
9050I53= 9050 - 3375 = 5675
5675 - 133
= 5675 - 2197 = 3478
3478 - 113= 3478 - 1331 = 2147
2147 - 93= 2147 - 729 = 1418
1418 - 73= 1418 - 343 = 1075 1077
Ans: (5)
9. 1 4 25 256 3125 46656 823543
(1)3125
(2) 823543
(3) 46656
(4) 25
(5) 256
Solution:The pattern of number series is as follows:
11= 1;-2
2= 4; 3
3= 27 25; 4
4= 256; 5
5= 3125; 6
6= 46656;
77= 823543
Ans: (4)
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10. 8424 4212 2106 1051 526.5 263.25 131.625
(1) 131.625
(2) 1051
(3) 4212
(4) 8424
(5) 263.25
Solution:The pattern of number series is as follows:
8424 2 = 4212
4212 2 = 2106
2106 2 = 1053 1051
1053 2 = 526.5
526.5 2 = 263.25
263.25 2 = 13 1.625
Ans: (2)
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Practice Set (Number Series)
Directions (Q. 1-3): What will come in place
of question mark (?) in the following
number series?(IBPS RRB Grade Officer
Exam 2012)
1. 987 587 331 187 123 (?)
(1) 104
(2) 113
(3) 107
(4) 114
(5) None of these
2. 125 171 263 401 585 (?)
(1) 835
(2) 815
(3) 792
(4) 788
(5) None of these
3.121 132 167 226 309 (?)
(1) 424
(2) 413
(3) 427
(4) 416
(5) None of these
Directions (Q. 4-5): In the following
number series, only one is wrong. Find out
the wrong number.
4.454 327 648 524 842 713 1036
(1) 327
(2) 648
(3) 521
(4) 842
(5) 713
5.72.5 86 113 168 275 491 923
(1) 86
(2)113
(3)168
(4)275
(5)491
Directions (Q. 6-10): What will come in
place of question mark (?) in the following
number series? (RBI GradeB Officers
Exam 2011)
6. 17 19 33 (?) 129 227
(1)64
(2)73
(3)67
(4)72
(5)None of these
7.35 256 451 620 763 (?)
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(1)680
(2)893
(3)633
(4)
880(5)None of these
8. 18 139 868 917 (?) 1051
(1)1042
(2)1036
(3)942
(4)996
(5)None of these
9. 2890 (?) 1162 874 730
658
(1)1684
(2)1738
(3)1784
(4)1672
(5)None of these
10. 14 1004 1202 1251.5 1268 (?)
(1)1267.5
(2)
1276.25(3)
1324.5
(4)1367.25
(5)
None of these
Directions (Q. 11-15): What will come in
place of question mark (?) in the following
number series?(Corporation Bank PO
2011)
11. 8 11 20 47 128 (?)
(1)483
(2)488
(3)397
(4)371
(5)None of these
12. 71 78 99 134 183 (?)
(1)253
(2)239
(3)246
(4)
253(5)None of these
13. 342 337.5 328.5 315 297 (?)
265.5
274.5
270
260
None of these
14. 161 164 179 242 497 (?)
(1)1540
(2)1480
(3)1520
(4)1440
(5)None of these
15. 239 254 284 344 464 (?)
(1)726
(2)716
(3)724
(4)714
(5)None of these
Directions-(Q. 16-20) What will come in
place of question-mark (?) in the following
number series?(Allahabad Bank
Probationary Officers Exam 2011)
16. 958 833 733 658 608, (?)
(1)
577
(2)583
(3)567
(4)573
(5)None of these
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17. 11 10 18 51 200, (?)
(1)885
(2)
1025(3)865
(4)995
(5)None of these
18. 25 48 94 186 370 (?)
(1)
738
(2)744
(3)746
(4)724
(5)
None of these
19. 14 24 43 71 108 (?)
(1)194
(2)
154(3)3) 145
(4)4) 155
(5)5) None of these
20. 144 173 140 169 136 (?)
(1)
157
(2)148
(3)164
(4)132
(5)
None of these
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Number Series Practice Set (Answers)
1) 3
2) 2
3) 4
4) 5
5) 36) 3
7) 4
8) 1
9) 2
10) 2
11) 4
12) 3
13) 2
14) 3
15) 516) 2
17) 4
18) 1
19) 2
20) 5
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Chapter: Number System
Introduction:
Number is a symbol which represents quantity. There are three types of numbers:
1.
Real Numbers:Real numbers are those numbers which can be easily indentify and
quantify.
For example: -10, -7.33, -1, 0, 1, 2, 5.77 etc.
2.
Imaginary Numbers:Imaginary numbers are those numbers which we can just imagine
but cannot physically perceive.
For example: , etc, is represented by i . Square root of all negative
numbers are imaginary.
3.
Complex Number:Combination of Real and Imaginary number is called complex
numbers.
For example:(2+5i) , (1+3i) etc .
Here we will only discuss about the real numbers .
Types of Real Numbers: there are two types of real numbers
1. Rational numbers:-All that numbers which can be expressed in the form of where p
& q are integers and q 0 are called rational numbers.
For example: - -1, 2, , 0, 1 , 2.7 etc. , here -1 = =
Again Rational numbers are classified as:
(a)
Integers:All rational numbers which do not have decimal or fractional parts are called
integers.For example: -3, -1, 0 , 1 , 2 etc .
Integers are of two type whole numbers and natural numbers. All the non negative integers are
whole numbers , for example 0 , 1 , 2 , 3 etc and all the whole numbers except 0 are natural
numbers , for example 1, 2 , 3 etc
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(b)
Fractions:All rational numbers which are in the form of where p & q are integers and
q 0 and p is not a multiple of q are called fractions.
For example: - 1.2, , , 1.7, .3 etc.
Fractions are of three types:
Proper
Improper
Mixed fractions
A proper fraction is a fraction whose numerator is smaller than denominator, for example
, etc. An improper fraction is a fraction whose numerator is equal to or greater than its
denominator for example , etc. and a mixed fraction is an integer plus a fraction, for
example , etc.
2.
Irrational Numbers:- All that numbers which cannot be expressed in the form of are
called irrational numbers. They have non-terminating and non-recurring decimal parts.
For example: , , etc.
On the basis of origin:
1. Prime Numbers:All the natural numbers greater than 1 which are only divisible by 1
and the number itself are called prime numbers.
For example:2, 3, 5, 7, 11, 13, 17 etc.
2.
Composite Numbers:All the natural numbers greater than 1 which are divisible by at
least one more number other than 1 and the number itself are called composite
numbers.
For example:4, 6, 8, 9, 10, 12 etc.
Note:1 is neither a prime number nor a composite.
On basis of divisor:
1.
Even Numbers:All the natural numbers which are multiple of 2 are called even
numbers.
For example:2, 4, 6, 8, 10 etc.
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Odd Numbers:All the natural numbers which are not a multiple of 2 are called odd
numbers. They are denoted as 2k 1, where k is a natural number.
For example:3, 5, 7, 9, 11 etc.
To find whether a number is prime or not.
Step 1:Find the approximate square root of a number .
Step 2:Check if any prime number from 2 to that square root divides that number or not.
Step 3:If none of those prime number divides the number than the number must be prime
number.
Example: Take 631 , the approx square root of 631 is 25 , now from 2 to 25 there are 2 , 3 ,5
, 7 , 11 , 13 , 17 , 19 and 23 prime number . Since none of these divides 631, so 631 must be
a prime number.
Conversion of recurring decimal into fraction.
The form of purely recurring number =
Let x = 0.77777. 10x = 7.77777
If x = 0.27272727 . 100 x = 27.272727
The form of purely recurring number =
Let x= 0.143333333.. 100x = 14.333333. 1000x = 143.3333.
= 129
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Quotient and remainder:
Dividend = (Divisor Quotient) + remainder.
For example:If dividend = 15968, Quotient = 89 and remainder = 37 then Divisor is?
Divisor =
=
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Divisibility Rules:
ForNumber Divisibility Rule Example Note
2 If the last digit of a number
is 0,2,4,6,8 , then the
number is divisible by 2
742 is divisible by 2 but 743 is
not.
3 If the sum of all the digits of
a number is divisible by 3 ,
then the number is divisible
by 3
1458 (sum of digits = 18) is
divisible by 3, but 766 (sum of
digits =19) is not divisible by 3.
766 (sum of digits
=19) the remainder
when 19 is divided by
3 i.e. 1 will also bethe remainder when
766 is divided by3
4 If the last two digits of a
number are divisible by 4,
then the number is also
divisible by 4
6732 is divisible by 4 as 32 is
divisible by 4, but 2142 is not
divisible by 4.
Similarly the
remainder when 42 is
divided by 4 i.e 2 will
also be the
remainder when
2142 is divided by 4.
5 If the last digits of a number
are 0 and 5, then the
number is divisible by 5.
1465, 1320 are divisible by 5
as their last digit is 5 and 0
respectively.
6 If the number is divisible by
2 and 3 both, then it is also
divisible by 6.
1452 is divisible by both 2 and
3 so it is divisible by 6 also,
but 3362 is not divisible by 6
as it is not divisible by 3.
If the number is
divisible by 4 and 6
both, then it is not
necessary that it is
divisible by 24 (6 4).
8 If the last three digit of a
number are divisible by 8 or
are 000, then the number is
divisible by 8 .
43102 and 13000 are divisible
by 8 since 102 is divisible by 8
and 13000 have 000 as last
three digits, but 2148 is not as
The remainder when
148 is divided by 8
i.e. 4 will also be the
remainder of 2148
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148 is not divisible by 8 when divided by 8.
9 If the sum of all digits of a
number is divisible by 9 ,
then the number is also
divisible by 9.
25344 (sum of digits = 18) is
divisible by 9 , 764 (sum of
digits =17) is not.
The remainder when
17 is divided by 9 i.e
8 will also be the
remainder when 764
is divided by 9.
11 If the difference between
the sum of the digits in the
even places and the sum of
the digits in the odd places
is either 0 or is divisible by
11 , then the number is also
divisible by 11.
9415956 is divisible by 11 as
the difference of 9+1+9+6 =25
and 4+5+5 = 14 is 11, but
31872 is not as the sum of
even places = 13 and sum of
odd is 8 their difference is
neither 0 nor 11.
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Solved Examples (Number System)
1. When X is subtracted from the numbers 9, 15 and 27, the remainders are in continued
proportion. What is the value of X?(IBPS CWE PO MT 2012)
(1) 8
(2) 6
(3) 4
(4) 5
(5) None of these
Solution:Let be subtracted from the numbers 9, 15 and 27 we get continue proportion.Now, 9 : 15 : 27
b2= ac
(15 )2= (9 ) (27 )
or, 22530 +2= 243 +
236
or, 6 = 243225 = 18
X = 3
Hence number become 9 - x = 9-3=6
15x = 15 -3 = 12
And 27-x = 27 -3 = 24
6 : 12 : 24 = 1: 2: 4Thus 1: 2: 4 is continued proportion
Ans: (5)
2. Sum of three consecutive numbers is 2262. What is 41% of the highest number?(IBPS CWE
PO MT 2012)
(1) 301.5.1
(2) 303.14
(3) 308.73
(4) 306.35
(5) 309.55
Solution:Let the three consecutive number be x, x + 1 and x + 2.
Then, x + x + 1 + x + 2 =2262
or, 3x = 22623 = 2259
x = = 753
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The Numbers are 753, 754, 755.
The highest number is 755
41% of 755 = 755 = 41 7.55 = 309.55
Ans: (5)
3. Rachita enters a shop to buy ice-creams, cookies and pastries. She has to buy at least 9
units of each. She buys more cookies than ice-creams and more pastries than cookies. She
picks up a total of 32 items. How many cookies does she buy? (IBPS CWE PO MT 2012)
(1) Either 12 or 13
(2) Either 11 or 12
(3) Either 10 or 11
(4) Either 9 or 11
(5) Either 9 or 10
Solution:
Total number of items = 32
Maximum number of ice creams = 9
pastries> cookies> ice cream
So, 13 10 9
12 11 9
Hence number of cookies is either 10 or 11.
Number of pastries is either 13 or 12.
Ans: (3)
4. The fare of a bus is Rs. x for the first five kilometres and Rs. 13/- per kilometre thereafter. If
a passenger pays Rs. 2402/- for a journey of 187 kilometres, what is the value of X? (IBPS CWE
PO MT 2012)
(1) Rs. 29
(2) Rs. 39
(3) Rs. 36
(4) Rs. 31
(5) None of these
Solution:Let the fare of first five kilometres be Rs. x.
Total distance = 187 km
Remaining distance = 187 - 5 = 182 km
Now, x + 182 13 = 2402
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x = 2402 - 2366= Rs.36
Ans: (3)
5. The product of three consecutive even numbers is 4032. The product of the first and thethird number is 252. What is five times the second number?
(1) 80
(2) 100
(3) 60
(4) 70
(5) 90
Solution:Let the three consecutive even numbers be 2x, 2x + 2 and 2x+4.
Then, (2x) (2x + 2) (2x + 4) = 4032 ... (I)
Again, product of first and third number
2x (2x + 4) = 252 ... (II)
Putting the values of the product of first and third number in eqn (I), we have
(2x + 2) 252 = 4032
or, 2x + 2 = = 16
x = 7
Hence, first number = 7 8 = 14
Second number = 7 x 2 + 2 = 16
And third number = 7 x 2 + 4 = 18
Five times of second number = 5 x 16 = 80
Ans: (1)
6. Rubina could get equal number of Rs. 55, Rs. 85 and Rs. 105 tickets for a movie. She spends
Rs. 2,940 for all the tickets. How many of each did she buy?
(1) 12
(2) 14
(3) 16
(4) Cannot be determined
(5) None of these
Solution:Let she buy x tickets.
Then total money spent = 55x + 85x + 105x
or, 245x = 2940
or, x = 12
Ans: (1)
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7. Seema bought 20 pens, 8 packets of wax colours, 6 calculators and 7 pencil boxes. The price
of one pen is Rs. 7, one packet of wax colour is for Rs. 22, one calculator is for Rs. 175 and one
pencil box costs Rs. 14 more than the combined price of one pen and one packet of wax
colours.How much amount did Seema pay to the shopkeeper?
(1) Rs. 1,491
(2) Rs. 1,725
(3) Rs. 1,667
(4) Rs. 1,527
(5) None of these
Solution:Price of one pencil box = 14 + (Price of one pen + Price of one packet of wax colours)=
14+ (7+22) = Rs. 43
Total amount paid by Seema= {(20 7) + (8 22) + (6 175) + (7 43)}
= Rs 1667
Ans: (3)
8. In a cricket match, Sachin and Viru scored a century each (more than 100 runs) and Yuvi
and Gauti scored a half century each. Gauti scored 76 runs and Yuvi scored 12 runs less than
Gauti. Viru scored 102 runs. The sum of the scores of all the four players is 442. How many
runs did Sachin score?(Corporation Bank PO 2011)
(1)200
(2)210
(3)180
(4)160
(5)None of these
Solution: Sachin's score = 44276(7612)102 = 200
Ans: (1)
9. The sum of seven consecutive even numbers of Set A is 378. What is the sum of a different
set of four consecutive numbers whose lowest number is 23 less than the mean of Set A?
(1)132
(2)146
(3)156
(4)124
(5)None of these
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Solution:Mean of Set A
Lowest number of Set B = (5423) = 31
Sum of the four numbers of Set B= 31 + 32 + 33 + 34 = 130
Ans: (5)
10. The sum of six consecutive even numbers of Set-A is 402. What is the sum of another Set-
B of four consecutive numbers whose lowest number is 15 less than double the lowest
number of set- A?(Allahabad Bank Probationary Officers Exam 2011)
(1)
444
(2)442
(3)
440(4)446
(5)
None of these
Solution: Third even number = = 67 - 1 = 66
smallest even number = 62
smallest number of set B = 2 x 62 - 15 = 109
required sum = 109 + 110 + 111+ 112 = 442
Ans: (2)
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Practice Set-1 (Number System)
1. A person on tour has Rs 360 for his daily expense. He decides to extend his tour
programme by 4 days which leads to cutting down daily expense by Rs 3 a day. The number
of days of his tour programme is
(1)15
(2)20
(3)18
(4)16
2. Two times a two-digit number is 9 times the number obtained by reversing the digits and
sum of the digits is 9. The number is
(1)72
(2)54
(3)63
(4)81
3. If 5 students utilize 18 pencils in 9 days, how long at the same rate will 66 pencils last for 15
students?
(1)10 days
(2)
12 days(3)
11 days
(4)None of these
4. A man has certain number of small boxes to pack into parcels. If he packs 3, 4, 5 or 6 in a
parcel, he is left with one over; if he packs 7 in a parcel, none is left over. What is the number
of boxes he may have to pack?
(1)106
(2)301
(3)
309
(4)
400
5. Out of a group of swans, 7/2 times the square foot of the number are playing on the shore
of the pond. The two remaining are inside the pond. What is the total number of swans?
(1)10
(2)14
(3)12
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(4)16
6. In a family, each daughter has the same number of brothers as she has sisters and each son
has twice as many sisters as he has brothers. How many sons are there in the family?
(1)
4
(2)3
(3)2
(4)5
7. A yearly payment to a servant is Rs. 90 plus one turban. The servant leaves the job after 9
months and received 65 and a turban. Then find the price of the turban.
(1)Rs 10
(2)Rs 15
(3)
Rs 7.50
(4)Cannot be determined
8. Mr. Mukherjee is 5 yr older to his wife and they have one son and one daughter. If the
daughter is 23 yr younger to his mother, what is the difference in the ages of the brother and
the sister?
(1)7 yr
(2)12 yr
(3)4 yr
(4)2 yr
9. The expenses of a hotel consist of two parts. The first one varies with the number of
inmates, while the second one is fixed. When the numbers of inmates are 275 and 350, the
expenses are Rs 1600 and Rs 1900 respectively. The expenses when the number of inmates is
315, are
(1)Rs 1760
(2)Rs 1680
(3)Rs 1780
(4)Rs 1660
10. If the numerator of a fraction is doubled and the denominator is increased by 3, the newfraction is 3/5 what is the original fraction, if its denominator is more than twice the
numerator by 1?
(1)3/7
(2)6/13
(3)1/3
(4)5/11
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Practice Set-2 (Number System)
1. The sum and product of two numbers are 5 and 6, respectively. The sum of reciprocals of
their squares is
(1)
(2)
(3)
(4)
2. The sum of the squares of 3 consecutive positive numbers is 365. The sum of the numbers
is
(1)30
(2)33
(3)36
(4)45
3. The sum of a natural number and its square equals the product of the first three primenumbers. The number is
(1)2
(2)3
(3)5
(4)6
4. 47 is added to the product of 71 and an unknown number. The new number is divisible by
7, giving the quotient 98. The unknown number is a multiple of
(1)2
(2)
7
(3)5
(4)3
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5. Two natural numbers are in the ratio 3: 5 and their product is 2160. The smaller of the
number is
(1)
36(2)24
(3)18
(4)12
6. The sum of two numbers is 10. Their product is 20. Find the sum of the reciprocals of the
two numbers.
(1)1
(2)
(3)
(4)
7. The sum of the digits of a two digit numbers is 10. The number formed by reversing the
digits is 18 less than the original number. Find the original number.
(1)81
(2)46
(3)64
(4)
60
8. The least number to be subtracted from 36798 to get a number which is exactly divisible by
78 is
(1)18
(2)60
(3)38
(4)68
9. The sum of first sixty number from one to sixty is divisible by
(1)
13(2)59
(3)60
(4)61
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10. Eight consecutive number are given. If the average of the two numbers that appear in the
middle is 6, then the sum of the eight given numbers is
(1)
36(2)48
(3)54
(4)64
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Number System Practice Set-1 (Answers)
1 (2)
2 (4)
3 (3)
4 (2)
5 (4)
6 (2)
7 (1)
8 (4)
9 (1)
10 (1)
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Number System Practice Set-2 (Answers)
1 (1)
2 (2)
3 (3)
4 (4)
5 (1)
6 (3)
7 (3)
8 (2)
9 (4)
10 (2)
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Chapter: Ratio, Proportion & Alligation
Introduction:-
Ratio is the relation which one quantity bears to another of the same kind. The ratio of two
quantities a and b is the fraction and we write it as a: b.
In the ratio a: b, we call a as the first term or antecedent and b, the second term or
consequent.
Note:The multiplication or division of each term of a ratio by the same non- zero number does
not affect the ratio.
Compound Ratio: -It is obtained by multiplying together the numerators for new numerator
and denominators for new denominator.
Example 1.If the ratios are 4:3, 15:20, 2:6 and 3:5 find the compound ratio?
Sol 1.Required ratio =
Duplicate ratio of a: b =
Triplicate ratio of a: b = etc.
Example2.If we divide 4185 into two parts such that they are in ratio 7:2, then find the values
of both the parts?
Sol 2.Let the actual variable be 7x and 2x.
Then 7x+2x = 4185
So, the 1st
part = 7
The 2nd
part = 2
Note:
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The ratio of first , second and third quantities is given by
ac : bc : bd
If the ratio between first and second quantity is a:b and third and fourth is c:d.
a: b
c: d
ac : bc : bd
Similarly, the ratio of first, second, third and fourth quantities is given by
ace : bce : bde : bdf
If the ratio between first and second quantity is a: b and third and fourth is c:d .
a : b
c : d
e : f
ace : bce : bde : bdf
Example 3.If Savita has Rs 1880. How much money does Ravina have if the ratio of money withsavita and Rita is 15: 7 and that with Rita and Ravina 16: 7?
Solution3:
Savita : Rita : Ravina
15 : 7
16 : 7
15
240 : 112 : 14
The ratio of money with Savita , Rita and Ravina is 240 : 112 : 14.
We see that 240 x = 1880
Hence 14
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Proportion
Introduction:-
Four quantities are said to be proportional if the two ratios are equal i.e. the A, B, C and
D are proportion. It is denoted by :: it is written as A : B : C : D where A and D are extremes
and B and C are called means .
Product of the extreme = Product of the means
Direct proportion: -The two given quantities are so related that if one quantity increases (or
decreases) then the other quantity also increases (or decreases).
Example 1. If 5 pens cost Rs 10 then 15 pen cost?
Sol 1. It is seen that if number of pens increases then cost also increases. So,
5 pens: 15 pens:: Rs 10 : required cost
Required cost =
Inverse proportion: -The two given quantities are so related that if one quantity increases (or
decreases) then the other quantity also decreases (or increases).
Example 2.If 10 men can do a work in 20 days then in how many days 20 men can do that work?
Sol 2. Here if men increase then days should decrease, so this is a case of inverse proportion, so
10 men: 20 men :: required days : 20 days
Required days =
Rule of three:It Is the method of finding 4thterm of a proportion if all the other three are given,if ratio is a:b :: c:d then ,
d =
Compound proportion: -Lets take an example to explain this.
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Example3. If 9 men can do a piece of work in 40 days of 10 hours each, how many men will it
take to do 12 times the amount of work if they work for 30 days of 9 hours?
Solution 3:
Step 1.Days: . : .
Hours: . : .. :: 9: required no. of men
Work: . : ..
Step 2.
1. Compare days with men : to do the work in less days we will need more men , so it is the
case of inverse proportion hence ,
30
: 40 :: 9 : required no. of men2. Compare hours with men : to do the work in less hours we will need more men , so it is
the case of inverse proportion hence ,
9 : 10 :: 9 : required no. of men
3. Compare work with men : to do the more work we will need more men , so it is the
case of direct proportion hence ,
1: 12:: 9: required no. of men
Put all the values in step 1,
30: 40
9: 10 :: 9: required no. of men
1: 12
Now,
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ALLIGATION
Introduction:-
The word allegation means linking. It is used to find:
1. The proportion in which the ingredients of given price are mixed to produce a new
mixture at a given price.
2. The mean or average value of mixture when the price of the two or more ingredients
and the proportion in which they are mixed are given.
Mathematical Formula:
For two ingredient:-
CP of unit quantity of cheaper (c) CP of unit quantity of dearer (d)
Mean Price
(d-m) (m-c)
Then (cheaper quantity): (dearer quantity) = (d-m): (m-c)
Example 1:If the rice at Rs 3.20 per kg and the rice at Rs 3.50 per kg be mixed then what
should be their proportion so that the new mixture be worth Rs 3.35 per kg ?
Sol 1:CP of 1 kg of cheaper rice CP of 1 kg of dearer rice
320 paisa 350 paisa
Mean Price (m)
335 paisa
15 15
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By allegation:
Hence they must be mixed in equal proportion i.e. 1:1
For three ingredient:-
1. The price of the ingredient should be reduced to one denomination and then place
them in ascending order under one another.
2. After that place the mean prices to the left of all the price
3. Then pair the price so that price less than and greater than the mean prices go together.
4. Then find out the difference between mean price and each price and place it opposite to
the price with which it is linked.
5. These difference will help to find out the given answer and similarly it will work for four
ingredients .
Example 2:Find out the ratio of new mixture so that it will cost Rs 1.40 per kg from the
given three kinds of rice costing Rs 1.20, Rs 1.45 and Rs 1.74?
Sol 2:1st
rice cost = 120, 2nd
rice cost = 145 and 3rd
rice cost = 174 paisa.
From the above rule: we have,
120 5+34 [(145-140) + (174-140)]
140 145 20 (140-120)
174 20 (140-120)
Therefore, three rice must be mixed in 39: 20: 20 ratios to have a new mixture of rice.
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Solved Examples (Ratio, Proportion & Alligation)
1. A certain amount was to be distributed among A, B and C in the ratio 2: 3: 4 respectively,
but was erroneously distributed in the ratio 7: 2: 5 respectively. As a result of this, B got Rs 40
less. What is the amount?(IBPS CWE PO MT 2012)
(1) Rs. 210
(2) Rs. 270
(3) Rs. 230
(4) Rs. 280
(5) None of these
Solution:Let the amount be x.
B's share =
Due to error B's share =
Difference in B's share due to error = 40
- = 40
or, = 40
or, 24x = 40 126
x = = Rs. 210
Ans: (1)
2. Rs.73,689/- are divided between A and B in the ratio 4: 7. What is the difference between
thrice the share of A and twice the share of B?(IBPS CWE PO MT 2012)
(1) Rs. 36,699
(2) Rs. 46,893(3) Rs. 20,097
(4) Rs. 26,796
(5) Rs. 13,398
Solution:Let As share be 4x and Bs share be 7x.
4x +7x = 73689
or, 11x = 73689
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x = = 6699
As share = 6699 4 = 26796
Bs share = 6699 7 = 44893
Thrice the share of A = 26796 3 = 80388
Twice the share of B = 46893 2= 93786
Difference = 93786 - 80388 = Rs. 13398
Ans: (5)
3. The ratio of the present age of Manisha and Deepali is 5:X. Manisha is 9 years younger than
Parineeta. Parineetas age after 9 years will be 33 years. The difference between Deepali's
and Manisha's age is the same as the present age of Parineeta. What should come in place of
X?
(1) 23
(2) 39
(3) 15
(4) Cannot be determined
(5) None of these
Solution:Parineetas present age = (33 - 9 =) 24 yrs.
Manisha's present age = (24 - 9 =) 15 yrs.
Deepalis present age = IS + 24 = 39 yrs.
Ratio of the present age of Manisha and Deepali
= 15 : 39 = 5 : 13
X = 13
Ans: (5)
4. The ratio between the three angles of a quadrilateral is 3 : 5 : 9. The value of the fourth
angle of the quadrilateral is 71. What is the difference between the largest and the smallest
angles of the quadrilateral?(IBPS RRB Group A Officers Exam 2012)
(1) 82
(2) 106
(3) 102
(4) 92
(5) None of these
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Solution.Let the quadrilateral angles be 3x, 5x, 9x and 71.
Total sum of angles = 3x + 5x + 9x + 71 = 360
or, 17x = 36071 = 289
x = 17Hence angles are 51, 85, 153, and 71.
Difference = 15351 = 102.
Ans: (3)
5. The second largest and the smallest angles of a triangle are in the ratio of 6 : 5. The
difference between the second largest angle and the smallest angle 'of the triangle is equal to
9. What is the difference between the smallest and the largest angles of the triangle? (IBPS
RRB Group A Officers Exam 2012)
(1) 36(2) 24
(3) 12
(4) 18
(4) None of these
Solution.Let the second largest angle of the triangle be 6x and the smallest angle 5x.
Now, 6x - 5x = 9
or, x = 9
Second largest angle = 54
Smallest angle = 45
Sum of angles of a triangle = 180
largest angle = 180 - 99 = 810
Difference = 81 - 45 = 36.
Ans:1
6. The ratio between the speed of a bus and train is 15 : 27 respectively. Also, a car covered adistance of 720 km in 9 hours. The speed of the bus is three- fourth the speed of the car. How
much distance will the train cover in 7 hours?(Allahabad Bank Probationary Officers Exam
2011)
(1) 760 km
(2) 756 km
(3) 740 km
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(4) Cannot be determined
(5) None of these
Solution:Speed of the car = = = 80hm/hr
Speed of the bus = 60km/hr
Speed of the train = 108km/hr
Distance covered by train in 7 hours = (7 x 108 =) 756 km
Ans: (2)
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Practice Set-1 (Ratio, Proportion & Alligation)
1.
A container has 80 L of milk. From
this container 8 L of milk was taken
out and replaced by water. The
process was further repeated twice.
The volume of milk in the container
after that is [SSC Quantitative
Aptitude (Arihant)]
a) 58.23 L
b)
85.23 L
c) 58.32 L
d) 85.32 L
2.
A can contains a mixture of two
liquids A and B in the ratio 7 : 5.
When 9 L of mixture is drawn off
and the can is filled with B, the
ratio of A and B becomes 7 : 9.
Litres of liquid A contained by the
can initially was
a) 10
b) 20
c) 21
d) 25
3.
What number should be added to
or subtracted from each term of the
ratio 17 : 24 so that it becomes
equal to 1 : 2?
a)
5 is subtracted
b) 10 is added
c) 7 is added
d) 10 is subtracted
4.
The ratio of weekly incomes of A
and B is 9 : 7 and the ratio of their
expenditures is 4 : 3. If each saves
Rs. 200 per week, then the sum of
their weekly incomes is
a) Rs. 3200
b) Rs. 4200
c) Rs. 4800
d) Rs. 5600
5.
The ratio of alcohol and water in 40
L of mixture is 5 : 3.8 L of the
mixture is removed and replaced
with water, Now, the ratio of the
alcohol and water in the resultant
mixture is
a) 1 : 2
b) 1 : 1
c) 2 : 1
d) 1 : 3
6.
Rama's expenditure and savings are
in the ratio 3 : 2. His income
increases by 10%. His expenditure
also increases by 12%. His saving
increases by
a) 7%
b) 10%
c) 9%
d) 13%
7.
Three numbers are in the ratio 3 : 4
: 5. The sum of the largest and the
smallest equals the sum of the
second and 52. The smallest
number is
a) 20
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b) 27
c) 39
d) 52
8.
The ratio of the ages of Ram and
Rahim 10 yr ago was 1 : 3. The ratio
of their ages 5 yr hence will be 2 : 3.
Then, the ratio of their present ages
is
a) 1 : 2
b) 3 : 5
c) 3 : 4
d) 2 : 5
9.
The ratio of milk and water in
mixtures of four container are 5 : 3,
2 : 1, 3 : 2 and 7 : 4, respectively. In
which container is the quantity of
milk, relative to water, minimum?
a) First
b) Second
c) Third
d) Fourth
10.
In a mixture of 25 L, the ratio of
acid to water is 4 : 1. Another 3 L of
water is added to the mixture. The
ratio of acid to water in the new
mixture is
a) 5 : 2
b)
2 : 5
c) 3 : 5
d) 5 : 3
11.
A shopkeeper buys two varieties of
tea, the price of the first being
twice the second. He sells the
mixture at Rs 36 per kilogram and
makes a profit of 20%. If the ratio of
quantities of the first and second
variety in these mixture is 3 : 4,
then what is the cost price of each
variety of tea ? [Mission MBA MAT
(Arihant)]
a) Rs 21, 42
b) Rs 15, 30
c) Rs 16.5, 33
d) Rs 17, 34
12.Two liquids are mixed in the ratio 3
: 5 and the mixture is sold at Rs 120
with a profit of 20%. If the first
liquid is costlier than the second by
Rs 2 per litre, find the cost of the
costlier liquid per litre.
a) Rs 92.30
b) Rs 74.10
c) Rs 101.25
d) Rs 99.25
13.A grocer buys two kinds of rice at
Rs 1.80 and Rs 1.20 per kg
respectively. In what proportion
should these be mixed, so that by
selling the mixture at Rs 1.75 per
kg, 25% may be gained?
a) 2 : 1
b) 3 : 2
c) 3 : 4
d)
1 : 2
14.A jar full of whisky contains 40% of
alcohol. A part of this whisky is
replaced by another containing 19%
alcohol and now the percentage of
alcohol was found to be 26. The
quantity of whisky replaced is
a)
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b)
c)
d)
15.
A container contains 240 L of wine.
80 L is taken out of the container
everyday and an equal quantity of
water is put into it. Find the
quantity of the wine that remains in
the container at the end of the
fourth day.a) 39.2 L
b) 32 L
c) 42.5 L
d) 47.40 L
16.
A tea trader mixed two varieties of
tea, one costing Rs 3.50 per kg and
the other costing Rs 4 per kg and
sells 40 kg of the mixture to a
vendor at Rs 4.50 per kg and makesa profit of 20%. How much of each
variety did the vendor mix?
a) 30 kg, 10 kg
b) 20 kg, 20 kg
c) 10 kg, 30 kg
d) None of these
17.
A vessel contains 50 L milk. The
milkman delivers 10 L to the first
house and adds an equal quantityof water. He does exactly the same
at the second and third house.
What is the ratio of milk and water
when he has finished delivering at
the third house?
a) 61 : 64
b) 27 : 37
c) 16 : 19
d) None of these
18.
Prabhu purchased 30 kg of rice at
the rate of Rs 17.50 per kg and
another 30 kg rice at a certain rate.
He mixed the two rice and sold the
entire quantity at the rate of Rs
18.60 per kg and made 20% over all
profit. At what price per kg did he
purchase the lot of another 30 kg
rice?
a)
Rs 14.50
b) Rs 12.50
c) Rs 15.50
d) Rs 13.50
19.
A person has a chemical of Rs 50
per litre. In what ratio should water
be mixed in that chemical so that
after selling the mixture at Rs 40
per litre he may get a profit of 50%.
a)
8 : 7
b)
9 : 8
c) 10 : 7
d) 4 : 3
20.
A trader has 50 kg of pulses, part of
which he sells at 8% profit and the
rest at 18% profit. He gains 14% on
the whole. What is the quantity
sold at 18% profit?
a)
30 kg
b) 35 kg
c) 40 kg
d) None of these
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21.
A container of capacity 120 L is
filled with milk and water. 80% of
milk and 40% of water is taken out
of vessel. It is found that the vessel
is vacated by 65%. What is the ratio
of milk to water?
a) 5 : 3
b) 6 : 5
c) 3 : 5
d) 4 : 3
22.
How much water should be added
to 60 L of milk at L for Rs 10 so
as to have a mixture worth Rs
per litre?
a) 16 L
b) 15 L
c) 18 L
d) 20 L
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Practice Set-2 (Ratio, Proportion & Alligation)
1.
An employer reduces the number
of employees in the ratio 8 : 5 and
increases their wages in the ratio 7 :
9. As a result, the overall wages bill
is
a) increased in the ratio 56 : 69
b) decreased in the ratio 56 : 45
c) increased in the ratio 13 : 17
d) decreased in the ratio 17 : 13
2.
A can contains a mixture of two
liquids A and B in the ratio 7 : 5.
When 9 L of mixture is drawn off
and the can is filled with B, the
ratio of A and B becomes 7 : 9.
Litres of liquid A contained by thecan initially was
e) 10
f) 20
g) 21
h) 25
3. What number should be added to
or subtracted from each term of the
ratio 17 : 24 so that it becomes
equal to 1 : 2?
e) 5 is subtracted
f) 10 is added
g) 7 is added
h) 10 is subtracted
4. The ratio of weekly incomes of A
and B is 9 : 7 and the ratio of their
expenditures is 4 : 3. If each saves
Rs. 200 per week, then the sum of
their weekly incomes is
e) Rs. 3200
f) Rs. 4200
g) Rs. 4800
h) Rs. 5600
5. Rama's expenditure and savings are
in the ratio 3 : 2. His income
increases by 10%. His expenditure
also increases by 12%. His saving
increases by
e) 7%
f) 10%
g) 9%
h)
13%
6.
If A : B is 2 : 3, B : C is 6 : 11, then A :
B : C is
a) 2 : 3 : 11
b) 4 : 6 : 22
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75 IBPS PO EXAM 2013 : Quantitative Aptitude
c) 4 : 6 : 11
d) 2 : 6 : 11
7. The ratio of the ages of Ram and
Rahim 10 yr ago was 1 : 3. The ratio
of their ages 5 yr hence will be 2 : 3.
Then, the ratio of their present ages
is
e) 1 : 2
f) 3 : 5
g)
3 : 4
h) 2 : 5
8.
If the annual income of A, B and C
are in the ratio 1 : 3 : 7 and the total
annual income of A and C is Rs.
800000, then the monthly salary of
B is
a)
Rs. 20000
b) Rs. 25000
c) Rs. 30000
d) Rs. 15000
9.
Two numbers are such that the
ratio between them is 4 : 7. If each
is increased by 4 the ratio becomes
3 : 5. The larger number is
a) 36
b) 48
c) 56
d) 64
10.Acid and water are mixed in a
vessel A in the ratio of 5 : 2 and inthe vessel B in the ratio of 8 : 5. In
what proportion should quantities
be taken out from the two vessels,
so as to form a mixture in which the
acid and water will be in the ratio
of 9 : 4?
a) 7 : 2
b)
2 : 7
c) 7 : 4
d) 2 : 3
11.
In an alloy, Zinc and Copper are in
the ratio 1 : 2. In the second alloy,
the same elements are in the ratio
2 : 3. If these two alloys be mixed to
form a new alloy in which twoelements are in the ratio 5 : 8, the
ratio of these two alloys in the new
alloy is
a) 3 : 10
b) 3 : 7
c) 10 : 3
d)
7 : 3
12.
A boy has a few coins of
denominations 50 paise, 25 paise
and 10 paise in the ratio 1 : 2 : 3. If
the total amount of the coins is Rs.
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76 IBPS PO EXAM 2013 : Quantitative Aptitude
6.50, the number of 10 paise coins
is
a)
5
b) 10
c) 15
d) 20
13.
The sum of the ages of a father and
his son is 100 yr now. 5 yr ago their
ages were in the ratio of 2 : 1. The
ratio of the ages of father and son
after 10 yr will be
a) 5 : 3
b) 4 : 3
c) 10 : 7
d) 3 : 5
14.
In a school having roll strength 286,
the ratio of boys and girls is 8 : 5. If
22 more girls get admitted into the
school, the ratio of boys and girls
becomes
a)
12 : 7
b) 10 : 7
c) 8 : 7
d) 4 : 3
15.
A box contains Rs. 1,50 paise and
25 paise coins in the ratio 8 : 5 : 3. If
the total amount of money in the
box is Rs. 112.50, the number of 50
paise coins is
a) 80
b) 50
c) 30
d) 42
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77 IBPS PO EXAM 2013 : Quantitative Aptitude
Ratio, Proportion & Alligation Practice Set-1 (Answers)
1) c
2) c
3) d
4) a
5) b
6) a
7)
c
8) b
9) c
10) a
11)
a
12) c
13) d
14) c
15) d
16) b
17) a
18)
d
19) a
20) a
21) a
22)
b
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78 IBPS PO EXAM 2013 : Quantitative Aptitude
Ratio, Proportion & Alligation Practice Set-2 (Answers)
1) b
2) c
3) d
4) a
5) a
6)
c
7) b
8) b