Ssc Cgl Tier II Solved Paper

7/30/2019 Ssc Cgl Tier II Solved Paper

1/17

Solved Paper

1

1. A General, while arranging his men, whowere 6000 in number, in the form of a square,found that there were 71 men left over. Howmany were arranged in each row?

(a) 73 (b) 77(c) 87 (d) 93

2. A number, when divided successively by 4,5 and 6, leaves remainders 2, 3 and 4respectively. The least such number is(a) 50 (b) 53(c) 19 (d) 214

3. A number, when divided by 296, gives 75 asthe remainder. If the same number is divided

by 37 then the remainder will be(a) 1 (b) 2(c) 19 (d) 31

4. The square root of3

2(0.75) 0.75 (0.75) 11 0.75

(a) 1 (b) 2(c) 3 (d) 4

5. The sum and product of two numbers are12 and 35 respectively. The sum of theirreciprocals will be

(a)1

3(b)

1

5(c)

12

35(d)

35

12

6. If

2 2

2 2

1 1

a b a b , then the value ofa2

+ b2

will be

(a) 1 (b)1

12

(c) 2 (d)1

22

7. If

21

xx

= 3, then

331x x

is equal to

(a) 3 (b) 2

(c) 1 (d) 0

8.0.1 0.1 0.1 0.02 0.02 0.02

0.2 0.2 0.2 0.04 0.04 0.04

is equal to

(a) 0.125 (b) 0.250(c) 0.500 (d) 0.855

9. If1

xx

= 2, then the value of100

100

1x

x is

(a) 2 (b) 0(c) 1 (d) 2

10. Ifx3 + 3x2 + 3x = 7, then x is equal to

(a) 2 (b) 3 6

(c) 1 (d) 1

11. If2

2xx

= 1, then the value of3

3

1x

x is

(a)13

8(b)

11

8(c)

11

8(d)

13

8

12. The greatest number among

3 5 75, 4 , 2, 3 is

(a) 3 4 (b) 7 3

(c) 5 (d) 5 2

SSCCombined Graduate Level TierII Exam

Held on: 01.08.2010
http://www.pdffactory.com/http://www.pdffactory.com/http://www.upscportal.com/


2/17

Solved Paper

2

13. 2 23 (13.608) (13.392) is equal to

(a) 0.6 (b) 0.06(c) 1.8 (d) 2.6

14.1 1 1 1

...1 2 2 3 3 4 99 100

is equal

to:

(a)1

9900(b)

99

100(c)

100

99(d)

1000

99

15. The sum of all the digits of the numbers from1 to 100 is(a) 5050 (b) 903

(c) 901 (d) 90016. A shopkeeper sells suger in such a way that

the selling price of 950g of sugar is the sameas the cost price of 1 kg of sugar. What is hisgain per cent?

(a)5

519

(b)1

55

(c) 5 (d)1

419

17. A person bought a horse and a carriage forRs. 20000. Later, he sold the horse at 20%profit and the carriage at 10% loss. Thus, hegained 2% in the whole transaction. The costprice of the horse was

(a) Rs. 7200 (b) Rs. 7500(c) Rs. 8000 (d) Rs. 9000

18. A sells an article to B at 15% profit. B sells itto C at 10% loss. If C pays Rs. 517.50 for itthen A purchased it at(a) Rs. 500 (b) Rs. 750(c) Rs. 1000 (d) Rs. 1250

19. An article is sold at a certai fixed price. By

selling it at2

3of that price, one loses 10%.

The gain per cent on selling it at the originalprice is

(a) 20 (b)1

333

(c)200

9(d) 40

20. A sells an ariticle to B for Rs. 45,000 losing10% in the transaction. B sells it to C at aprice which would have given a profit of10% to A. By what per cent does B gain?

(a)75

2(b)

100

3(c)

200

9(d)

150

7

21. The cost price of an article is 80% of itsmarked price for sale. How much per centdoes the tradesman gain after allowing adiscount of 12% ?(a) 20 (b) 12(c) 10 (d) 8

22. A merchant has announced 25% rebate on

prices of ready-made garments at the timeof sale. If a purchase needs to have a rebateof Rs. 400, then how many shirts, eachcosting Rs. 320, should he purchase?(a) 10 (b) 7(c) 6 (d) 5

23. A merchant purchases a wristwatch for Rs.450 and fixes its list price in a such a waythat after allowing a discount of 10%, heearns a profit of 20%. Then the list price (inrupees) of the wristwatch is(a) 500 (b) 600(c) 750 (d) 800

24. A reduction of 10% in the price of tea enablesa dealer to purchase 25 kg more tea for Rs.22500. What is the reduced price per kg oftea?(a) Rs. 70 (b) Rs. 80(c) Rs. 90 (d) Rs. 100

25. Ram donated 4% of his income to a charityand deposited 10% of the rest in a Bank. Ifnow he has Rs. 8640 left with him, then hisincome is(a) Rs. 12,500 (b) Rs. 12,000(c) Rs. 10,500 (d) Rs. 10,000

26. If the length of a rectangle is increased by

10% and its breadth is decreased by 10%,then its area(a) decreases by 1% (b) increases by 1%(c) decreases by 2%(d) remains unchanged


3/17

Solved Paper

3

27. Three spherical balls of radius 1 cm, 2 cmand 3 cm are melted to form a singlespherical ball. In the process, the loss ofmaterial is 25%. The radius of the new ballis(a) 6 cm (b) 5 cm(c) 3 cm (d) 2 cm

28. If A : B = 2 : 3, B : C = 4 : 5 and C : D = 5 : 9, thenA : D is equal to(a) 11 : 17 (b) 8 : 27(c) 5 : 9 (d) 2 : 9

29. If the length of a rectangle is increased inthe ratio 6 : 7 and its breadth is diminishedin the ratio 5 : 4 then its area will be

diminished in the ratio(a) 17 : 16 (b) 15 : 14(c) 9 : 8 (d) 8 : 7

30. 7 years ago, the ages (in years) of A and Bwere in the ratio 4 : 5; and 7 years hence theywill be in the ratio 5 : 6. The present age of Bis(a) 56 years (b) 63 years(c) 70 years (d) 77 years

31. Two numbers are such that theirdifference,their sum and their product arein the ratio of 1 : 7 : 24. The product of the

numbers is(a) 24 (b) 36(c) 48 (d) 60

32. A, B, C are partners in a business. During aparticular year, A received one third of theprofit, B received one fourth of the profit andC received the remaining Rs. 5000. Howmuch amount of money did a receive ?(a) Rs. 1000 (b) Rs. 3000(c) Rs. 4000 (d) Rs. 5000

33. Three horses are tethered at 3 corners of atriangular plot of land having sides 20m,30m and 40m each with a rope of length 7m.The area (in m2) of the region of this plot,which can be grazed by the horses, is

22Use

7

(a)77

3(b) 75 (c) 77 (d) 80

34. A wire, when bent in the form of a square,encloses a region of area 121 cm2. If the samewire is bent into the form of a circle, then the

area of the circle is22

Use7

(a) 150 cm2 (b) 152 cm2(c) 154 cm2 (d) 159 cm2

35. The ratio of the area of a sector of a circle tothe area of the circle is 1 : 4. If the area of thecircle is 154 cm2, the perimeter of the sector

is(a) 20 cm (b) 25 cm(c) 36 cm (d) 40 cm

36. The length of the diagonal of a cube is 6 cm.The volume of the cube (in cm3) is

(a) 18 3 (b) 24 3

(c) 28 3 (d) 30 3

37. If a sphere of radius r is divided into fouridentical parts, then the total surface area ofthe four parts is(a) 4 r2 square unit (b) 2 r2 square unit(c) 8 r2 square unit (d) 3 r2 square unit

38. A sum of money, deposited at some rate percent per annum of compound interest,doubles itself in 4 years. In how many yearswill it become 16 times of itself at the samerate ?(a) 16 (b) 12(c) 10 (d) 8

39. What is the difference between thecompound interest and simple interest onRs. 4000 at 5% per annum for 2 years ?(a) 10 (b) 11(c) 20 (d) 100

40. The simple and compound interests on asum of money for 2 year are Rs. 8400 andRs. 8652 respectively. The rate of interest perannum is(a) 6% (b) 7.5% (c) 9% (d) 4.5%


4/17

Solved Paper

4

41. A man can row against the current three-fourth of a kilometre in 15 minutes andreturns the same distance in 10 minutes. Theratio of his speed to that of the current is(a) 3 : 5 (b) 5 : 3(c) 1 : 5 (d) 5 : 1

42. Two places A and B are 100 km apart on ahighway. One car starts from A and anotherfrom B at the same time. If the cars travel inthe same direction at a constant speed, theymeet in 5 hours. If the cars travel towardseach other, they meet in 1 hour. What is thespeed of the car running faster ?(a) 60 km/hr. (b) 50 km/hr.

(c) 40 km/hr. (d) 32 km/hr.43. A can complete a piece of work in 12 days. B

is 60% more efficient than A. The number ofdays, that B will take to complete the samework, is

(a) 6 (b)1

72

(c) 8 (d)1

82

44. Two pipes can fill an empty tank separatelyin 24 minutes and 40 minutes respectivelyand a third pipe can empty 30 gallons ofwater per minute. If all the three pipes areopen, empty tank becomes full in one hour.

The capacity of the tank (in gallons) is(a) 800 (b) 600(c) 500 (d) 400

45. A batsman, in his 12th innings, makes a scoreof 63 runs and thereby increases his averagescore by 2. The average of his score after 12thinnings is(a) 41 (b) 42(c) 34 (d) 35

46. The greatest number, that divides 43, 91 and183 so as to leave the same remainder ineach case, is

(a) 9 (b) 8(c) 4 (d) 3

47.

7

16 6 7 16 6 7 is equal to

(a)1

2(b)

1

3(c)

1

4(d)

1

548. The sum of the areas of the 10 squares, the

lengths of whose sides are 20 cm, 21 cm, ... .29 cm respectively is(a) 6085 cm2 (b) 8555 cm2

(c) 2470 cm2 (d) 11025 cm2

49. The square root of

9.5 0.0085 18.9

0.0017 1.9 2.1

is

(a) 15 (b) 45(c) 75 (d) 225

50. If 123

xx

= 6, then 132

xx

is equal to

(a) 4 (b) 8(c) 9 (d) 12

51. If x = 122 1 then the value of2

2

1x

x

is

(a) 2 (b) 2 2

(c) 2 2 (d) 2

52.3 1 2 2 6 12

1 1 1 1 14 3 5 5 7 13

is

equal to

(a)2

13(b)

1

7(c)

1

6(d)

1

5

53.

3 3

2 2

(0.87) (0.13)

(0.87) (0.13) (0.87) (0.13)

is equal to

(a)1

2(b) 2 (c) 1 (d)

12

2

54. Ifx2 +y2 2x + 6y + 10 = 0, then the value of(x2 +y2) is(a) 4 (b) 6(c) 8 (d) 10


5/17

Solved Paper

5

55. The largest among the numbers

7 5, 5 3, 9 7 , 11 9 is

(a) 7 5 (b) 5 3

(c) 9 7 (d) 11 9

56. Ifx1/3 +y1/3 =z1/3, then (x +y z)3 + 27xyzis equal to(a) 0 (b) 1(c) 1 (d) 27

57. If 7 7 7 7.... = (343)y 1

theny is equal to

(a) 23

(b) 1

(c)4

3(d)

3

4

58. Ifa2 = 2, then (a + 1) is equal to

(a) a 1 (b)2

1a

(c)1

3 2

a

a

(d)

1

3 2

a

a

59. The missing term in the sequence 2, 3, 5, 7,11, ... 17, 19 is

(a) 16 (b) 15(c) 14 (d) 13

60. The wrong number in the sequence(a) 32 (b) 47(c) 63 (d) 83

61. When the price of a toy was increased by20%, the number of toys sold was decreased

by 15%. What was its effect on the total salesof the shop?(a) 2% increase (b) 2% decrease(c) 4% increase (d) 4% decrease

62. A person sold a horse at a gain of 15%. Had

he bought it for 25% less and sold it for Rs.60 less, he would have made a profit of 32%.The cost price of the horse was(a) Rs. 370 (b) Rs. 372(c) Rs. 375 (d) Rs. 378

63. A sells an article to B at a gain of 25% B sellsit to C at a gain of 20% and C sells it to D ata gain of 10%. If D pays Rs. 330 for it, howmuch did it cost to A ?(a) Rs. 200 (b) Rs. 250(c) Rs. 275 (d) Rs. 290

64. By selling an article for Rs. 21, a man lostsuch that the percentage loss was equal tothe cost price. The cost priceof the article was(a) Rs. 30 or Rs. 70 (b) Rs. 35 or Rs. 60(c) Rs. 45 (d) Rs. 50

65. Half of 100 articles were sold at a profit of20% and the rest at a profit of 40%. If all thearticles had been sold at a profit of 25%, the

total profit would have been Rs. 100 lessthan earlier profit. The cost price of eacharticle was(a) Rs. 10 (b) Rs. 15(c) Rs. 20 (d) Rs. 30

66. The market price of a clock is Rs. 3200. It isto be sold at Rs. 2448 at two successivediscounts. If the first discount is 10%, thenthe second discount is(a) 5% (b) 10%(c) 15% (d) 20%

67. A dealer marks his goods 30% above his costprice and then allows 15% discount on it.What is the cost price of an article on whichhe gains Rs. 84 ?(a) Rs. 800 (b) Rs. 560(c) Rs. 373.33 (d) Rs. 280

68. A shopkeeper wishes to give 5% commissionon the marked price of an article but alsowants to earn a profit of 10%. If his cost priceis Rs. 95, then the marked price is(a) Rs. 100 (b) Rs. 110(c) Rs. 120 (d) Rs. 130

69. Krishnamurthy earns Rs. 15000 per monthand spends 80% of it. Due to pay revision,

his monthly income has increased by 20%,but due to price rise, he has to spend 20%more. His new savings are(a) Rs. 3400 (b) Rs. 3000(c) Rs. 4600 (d) Rs. 4000


6/17

Solved Paper

6

70. Two numbers are respectively1

12 %2

and

25% more than a third number. The firstnumber is how much per cent of the secondnumber ?(a) 90 (b) 87.5(c) 25 (d) 12.5

71. Population of a town increases 2.5%annually but is decreased by 0.5% every yeardue to migration. What will be thepercentage of increase in 2 years?(a) 5 (b) 4.04(c) 4 (d) 3.96

72.72% of the students of a certain class tookBiology and 44% took Mathematics. If eachstudent took at least one of Biology orMathematics and 40 students tookboth ofthese subjects, the total number of studentsin the class is(a) 200 (b) 240(c) 250 (d) 320

73. Rs. 1050 are divided among A, B and C in

such a way that the share of A is2

5of the

combined share of B and C. A will get

(a) Rs. 200 (b) Rs. 300(c) Rs. 320 (d) Rs. 420

74. The sides of a right-angled triangle formingright angle are in the ratio 5 : 12. If the areaof the triangle is 270 cm2, then the length ofthe hypotenuse is(a) 39 cm (b) 42 cm(c) 45 cm (d) 51 cm

75. Two numbers are in the ratio 5 : 6. If theirH.C.F is 4, then their L.C.M. will be(a) 90 (b) 96(c) 120 (d) 150

76. Ifa + b + c = 1 and ab + bc + ca = 13 then a : b :

c is(a) 1 : 2 : 2 (b) 2 : 1 : 2(c) 1 : 1 : 1 (d) 1 : 2 : 1

77. A and B enter into partnership with capitalsin the ratio 5 : 6. At the end of 8 months Awithdraws his capital. They recived profitsin the ratio 5 : 9. Binvested the capital for(a) 6 months (b) 8 months(c) 10 months (d) 12 months

78. What is the length of the radius of the circum-circle of the equilateral triangle, the length

of whose side is 6 3 cm ?

(a) 6 3 cm (b) 6 cm

(c) 5.4 cm (d) 3 6 cm

79. If the measure of a diagonal and the area of

a rectangle are 25 cm and 168 cm

2

respectively, what is the length of therectangle ?(a) 31 cm (b) 24 cm(c) 17 cm (d) 7 cm

80. The number of coins, each of radius 0.75 cmand thickness 0.2 cm, to be melted to make aright circular cylinder of height 8 cm andradius 3 cm, is(a) 640 (b) 600 (c) 500 (d) 480

81. If the radius of a sphere is increased by 2m,its surface-area is increased by 704 m2.What is the radius of the original sphere?

22Use

7

(a) 16 m (b) 15 m (c) 14 m (d) 13 m

82. A right circular cylinder is circumscribing ahemisphere such that their bases arecommon. The ratio of their volumes is(a) 1 : 3 (b) 1 : 2(c) 2 : 3 (d) 3 : 4

83. A man invested1

3of his capital at 7%,

1

4at

8% and the remaining at 10% rate of simpleinterest. If his annualincome from interestsis Rs. 561, the capital invested was(a) Rs. 6000 (b) Rs. 5600(c) Rs. 6600 (d) Rs. 7200


7/17

Solved Paper

7

84. The compound interest on Rs. 6250 at 12%per annum for 1 year, compounded half-yearly is(a) Rs. 772.50 (b) Rs. 772(c) Rs. 672.50 (d) Rs. 672

85. A sum of money lent at compound interestamounts to Rs. 1460 in 2 years and to Rs.1606 in 3 years.The rate of interest perannum is(a) 12% (b) 11%(c) 10.5% (d) 10%

86. If A travels to his school from his house atthe speed of 3 km/hr. then he reaches theschool 5 minutes late. If he travels at the

speed of 4 km/hr, he reaches the school 5minutes earlier than school time. Thedistance of his school from his house is(a) 1 km (b) 2 km(c) 3 km (d) 4km

87. A train travelling with a speed of 60 km/hrcatches another train travelling in the samedirection and then leaves it 120 m behind in18 seconds. The speed of the second train is(a) 26 km/hr (b) 35 km/hr(c) 36 km/hr (d) 63 km/hr

88. A and B together can complete a piece of

work in 12 days and B and C together in 15days. If A is twice as good a workman as C,then in how many days will be alonecomplete the same work ?(a) 30 (b) 25(c) 24 (d) 20

89. 4 men and 6 women together can completea work in 8 days while 3 men and 7 womentogether can complete it in 10 days. 20women working together will complete it in(a) 36 days (b) 32 days(c) 24 days (d) 20 days

90. The average of two numbers A and B is 20,that of B and C is 19 and of C and A it is 21.What is the value of A?(a) 24 (b) 22(c) 20 (d) 18

Directions (91-95): The pie chart given below, showsthe expenditure on various items and savings of afamily during the year 2009. Study the pie chartand answer these questions.

PERCENTAGE OF MONEY SPENT ON VARIOUS

ITEMS AND SAVINGS BY A FAMILY DURING 2009

Others20%

Savings15%

Food 23% Clothing10%

Educationof Children

12%

Transport5%

Housing10%

91. If the total income of the family for the year2009 was Rs. 1,50,000 then the difference

between the expenditures on housing andtransport was(a) Rs. 15,000 (b) Rs. 10,000(c) Rs. 12,000 (d) Rs. 7,500

92. Maximum expenditure of the family otherthan on food, was on

(a) Housing (b) Clothing(c) Others(d) Education of children

93. The savings of the family for the year wereequal to the expenditure on(a) Food (b) Housing(c) Education of children(d) Clothing

94. The percentage of the income which wasspent on clothing, education of children andtransport together is(a) 17 (b) 20(c) 22 (d) 27

95. If the total income of the family was Rs.1,50,000 then the money spent on food was(a) Rs. 20,000 (b) Rs. 23,000(c) Rs. 30,000 (d) Rs. 34,500


8/17

Solved Paper

8

Directions (96-100): Study the bar diagram andanswer these questions.

1200

1000

800

600

400

200

2009200820072006

300

150

200 200

800900

1200

Numberofpersons

Persons killed in industrial accident

Persons killed in coal mines

96. The number of persons killed in coal minesin 2006 was what per cent of those killed inindustrial accidents in that year ?(a) 4 (b) 25(c) 36 (d) 300

97. In which year, minimum number of personswere killed in industrial accidents and coalmines together?(a) 2006 (b) 2007(c) 2008 (d) 2009

98. In which year, maximum number of personswere killed in industrial accidents other thanthose killed in coal mines?(a) 2006 (b) 2007(c) 2008 (d) 2009

99. In which years, minimum number ofpersons were killed in coal mines other thanthose killed in industrial accidents?(a) 2006 (b) 2007(c) 2008 (d) 2009

100. In a year, on average, how many personswere killed in industrial accidents and coal

mines together ?(a) 121.25 (b) 1212(c) 1212.5 (d) 1000

ANSWERS

1. (b) 2. (d) 3. (a) 4. (b) 5. (c)

6. (c) 7. (d) 8. (a) 9. (a) 10. (c)

11. (b) 12. (c) 13. (c) 14. (b) 15. (c)

16. (a) 17. (c) 18. (a) 19. (c) 20. (c)

21. (c) 22. (d) 23. (d) 24. (c) 25. (d)

26. (a) 27. (c) 28. (d) 29. (d) 30. (d)

31. (c) 32. (c) 33. (c) 34. (c) 35. (b)

36. (d) 37. (c) 38. (a) 39. (a) 40. (a)

41. (d) 42. (a) 43. (b) 44. (d) 45. (a)

46. (c) 47. (a) 48. (a) 49. (a) 50. (c)

51. (a) 52. (b) 53. (c) 54. (d) 55. (b)

56.(a)

57.(c)

58.(d)

59.(d)

60.(b)

61. (a) 62. (c) 63. (a) 64. (a) 65. (c)

66. (c) 67. (a) 68. (b) 69. (*) 70. (a)

71. (b) 72. (c) 73. (b) 74. (a) 75. (c)

76. (c) 77. (d) 78. (b) 79. (b) 80. (a)

81. (d) 82. (c) 83. (c) 84. (a) 85. (d)

86. (d) 87. (c) 88. (d) 89. (d) 90. (d)

91. (a) 92. (c) 93. (b) 94. (d) 95. (d)

96. (b) 97. (d) 98. (a) 99. (b) 100. (c)

EXPLANATIONS

1. Number of men arranged in the form of a

square= 6000 71 = 5929

Number of men arranged in each row

= 5929 = 77

2. 4 x Remainder

5y 2

6z 3

1 4

z = 6 1 + 4 = 10

y = 5 10 + 3 = 53

x = 4 53 + 2 = 214

4.

32(0.75) [(0.75) 0.75 1 1]

1 0.75


9/17

Solved Paper

9

=

3 2 2(0.75) (1 0.75)[(0.75) 0.75 1 1 ]

1 0.75

=3 3 3(0.75) 1 (0.75)

0.25

[(a b)(a2 + ab + b2) = a3 b3]

=1

1 0.75=

1

0.25=

100

25= 4

Square root = 4 = 2

5. x +y = 12 ...(i)

xy = 35 ...(ii)

x y

xy

=

1 1

y x =

12

35

6.2 2

2 2

1 1a b

a b = 4

2 2

2 2

1 1a b

a b = 4

2 21 1

2 2a ba b

= 4

2 21 1a b

a b

= 0

1

aa

= 0,1

bb

= 0

a = b = +1

a2 + b2 = 1 + 1 = 2.

7.

21

xx

= 3

1

xx

=3

Now,3

3

1x

x

=

31 1 1

3 .x x xx x x

= 33 3 3= 3 3 3 3 = 0

8. If 0.1 = 1 then, 0.2 = 2a

and 0.02 = b then, 0.04 = 2b

Expression

=2 2 2 2 2 2

a a a b b b

a a a b b b

=3 3

3 38 8a ba b

=

3 3

3 38( )a ba b

= 1

8= 0.125

10. x3 + 3x2 + 3x = 7

x3 + 3x2 + 3x + 1 = 7 + 1 = 8

(x + 1)3 = 23

x + 1 = 2

x = 1

11.2

2xx

= 1

1

x x

=

1

2 ...(i)

3

3

1x

x

=

31 1 1

3. .x x xx x x

=

31 1

32 2

=1 3

8 2 =

1 12

8

=

11

8

12. LCM of the orders of the surds = LCM of 2, 3,5 and 7 = 210

1

25 =105

2105 = 1105 2105


10/17

Solved Paper

10

1

34 =

70

2104 = 1

70 210

4

1

52=

42

2102= 142 2102

1

73 =30

2103 = 130 2103 The largest number

=1

25 = 5

13. Expression

= 2 23 (13.608) (13.392)

= 3 (13.608 13.392)(13.608 13.392)

= 3 27 0.216

= 327 216

1000

=3 6

10

=1.8

16. Profit per cent

= Trueweight Falseweight 100Falseweight

=1000 950

100950

=100

19=

55

19

17. If the GP of horse be Rs. x, then

CP of carriage = Rs. (20000 x)

120 90

(20000 )100 100

x x

=102

20000100

120x + 1800000 90x

= 204000

30x = 2040000 1800000= 240000

x =240000

30= Rs. 8000

18. If an article is old to B at x% profit/loss andB sells the same to C aty% profit/loss, thenCs C.P.

= As CP100100

100 100

yx

As CP = Cs CP

100 100100 15 100 10

=100 100

517.50115 90

= Rs. 500

19. Let the C.P. of the article be Rs. 100.

S.P. of the article 2

3= 90

S.P. of the article

=90 3

2

= 135

Profit per cent at the original price = 35

20. As C.P.

=100

4500090

= Rs. 50000

Bs S.P.

=110

50000100

= Rs. 55000

Bs profit per cent

= 10000 10045000

= 2009

21. C.P. of the article = Rs. 100

Marked price


11/17

Solved Paper

11

=100 100

80

= Rs. 125

SP after the discount

=125 88

Rs.100

= Rs. 110

Gain per cent = 10

23. If the marked price of the wrist watch be Rs.x, then

90

100x =

450 120

100

= 540

x =540 100

90

= Rs. 600

24. Let the original price of tea be Rs. x/kg

New price = Rs.9

/kg10

x

22500 225009

10

x x

= 25

10 1

225009x x

= 25

10 9

225009x

= 25

22500 = 25 9x

x =22500

25 9= 100

New price

=9

10010

= Rs. 90 per kg.

25. Let Rams income = Rs. 100.

Donation to charity = Rs. 4Amount deposited in bank

=96 10

100

= Rs. 9.6

Savings = 100 13.6 = Rs. 86.4

Q Rs. 86.4 = 100

Rs. 8640 =100

864086.4

= Rs. 10000

26. Effect on area

=10 10

10 10 %100

= 1%

Here, nevative sign shows decrease.

27. Volume of the new ball

=3 3 3

1 2 33 4

( )4 3

r r r

= (13+ 23 + 33)

= (1 + 8 + 27)

= 36p cubic cm.

34

3r = 36

r3 =36 3

4

= 27

r = 3

27= 3 cm

30. 7 years ago, As age = 4x years and Bs age =5x years

4 14

5 14

x

x

=

5

6

25x + 70 = 24x + 84

x = 84 70 = 14

Bs present age

= 5x + 7 = 5 14 + 7 = 77 years

32. Total profit 1 1

13 4

= 5000

Total profit 12 4 3

12

= 5000

Total profit


12/17

Solved Paper

12

=5000 12

5

= Rs. 12000

As share = Rs.1

120003

= Rs. 4000

34. Side of the square

= 121 = 11 cm

Length of the wire = 4 11

= 44 cm

2 r = 44

222 7 r = 44

r = 7 cm

Area of circle = r2

=22

7 77

= 154 sq. cm.

36. If the age edfe of the cube be x cm then,

3x = 6

x =

6

3 = 2 3 cm

Volume of the cube = (edge)3

= 2 3 2 3 2 3

= 24 3 cm3

37. Required total surface area

= 4 r2 + 4 r2

= 8 r2 sq.unit

39. Difference

= Principal

2

100

r

=

25

4000

100

= Rs. 10

40. Difference = Rs. (8652 8400) = Rs. 252

Rate =2 Difference

100S.I.

=2 252

1008400

= 6%

43. Ratio of their efficiency

= 100 : 160 = 5 : 8

Ratio of time taken = 8 : 5

Time taken by B

=5

128

=15

2=

17

2days

44. Capacity of the tank = x gallons.

Part of the tank filled in 1 minute

= 3024 40

x x

60 3024 40

x x = x

24 40 60

x x x = 30

5 3 2

120

x x x= 30

20

x=30 x = 600 gallons

45. Average of the batsman upto 11th innings= 63 12 2 = 39

Required average = 39 + 2 = 41

46. Required number

= HCF of (91 43), (183 91) and (183 43)

= HCF of 48, 92 and 140 = 4

47. Expression

=7

16 6 7 16 6 7

=7

9 7 2 3 7 9 7 2 3 7

=7

(3 7 ) (3 7 )


13/17

Solved Paper

13

=

7

3 7 3 7 =

1

2

48. Required sum = 202 + 212 + ... + 292

= (12 + 22 + ... + 292) (12 + 22 + ... + 192)

=29(29 1)(2 29 1) 19(19 1)(2 19 1)

6 6

2 2 2 ( 1)(2 1)1 2 ...6

n n nn

Q

= 8555 2470

= 6085 sq.cm.

49. Expression

=9.5 0.0085 18.9

0.0017 1.9 2.1

= 225

Required square root

= 225 = 15

51. x = 122 1 x 2 = 2 1

x2 = 12 1

= 1 2 12 1 2 1

= 2 1

21

x= 2 1

2

2

1x

x = 2 1 2 1 = 2

52. Expression

=3 4 5 3 13 1

4 3 3 5 7 13

=1

753. If 0.87 = a and 0.13 = b then,

Expression =3 3

2 2

a b

a b ab

=

2 2

2 2

( )( )a b a b ab

a b ab

= a + b = 0.87 + 0.13 = 1

54. x2 2x +y2 + 6y + 10 = 0

x2 2x + 1 +y2 + 6y + 9 = 0

(x 1)2 + (y + 3)2 = 0

= x 1 = 0 x = 1

and,y + 3 = 0 y = 3

x2 +y2 = 1 + 9 = 10

55. 7 5 = 7 5 7 5

7 5

=2

7 5

Similarly,

5 3 =2

5 3

9 7 =2

9 7

11 9 =2

11 9 Largest number = 5 3

because its denominator is the smallest.

56.1 1

3 3x y =1

3z

Cubing both sides, we have,

3 31 1 1 1 1 1

3 3 3 3 3 33. .x y x y x y

=z

x +y + 3.

1 1 1

3 3 33. . .x y x y z =z

(x +y z) =1 1 1

3 3 33. . .x y z


14/17

Solved Paper

14

Cubing again,

(x +y z)3

= 27 xyz (x +y z)3 + 27 xyz = 0

57. Let x = 7 7 7 7....

On squaring both sides,

x2 = 7x3

x2 7x = 0 x(x 7) = 0

x = 7

7 = (73) y 1 = 73y 3

3y 3 = 1

3y = 4

y =4

3

58. a2 = 2

a = 2

a + 1 = 2 1

From alternative (4)

1

3 2

a

a

=

2 1

3 2 2

= 2 1 3 2 23 2 2 3 2 2

=3 2 3 4 2 2

9 8

= 1 2

59. It is sequence of first prime numbers.

60. 8 + 5 = 13

13 + 8 = 21

21 + 11 = 32

32 + 14 = 46 47

46 + 17 = 63

61. Effect on sale

=20 15

20 15 %100

= 2% increase

62. If the CP of horse be Rs. x

then its SP = 115100

x

New CP =3

Rs.4

x

115

60100

x

=3 132

4 100x =

99

100

x

115 99

100 100

x x = 60

16

100

x= 60

x =60 100

16

= Rs. 375

63. As CP =100 100 100

330125 120 110

= Rs. 200

64. If the CP of article be Rs. x, then

21 100xx

= x3

x2 100x + 2100 = 0

x2 70x 30x + 2100 = 0

x (x 70) 30 (x 70) = 0

(x 30) (x 70) = 0

x = Rs. 30 or Rs. 70

65. Let the CP of each article be Rs. x.

5 120 50 140 100 125

100 100 100

x x x = 100

60x + 70x 125x = 100

5x = 100

x =100

5= Rs. 20


15/17

Solved Paper

15

67. CP of article = Rs.

Marked price

=130

100

x= Rs.

13

10

x

S.P.

=13 85

10 100

x = Rs.

221

200

x

221

200

xx = 84

221

200

x= 84

x =84 200

21

=Rs. 800

68. Marked price = Rs. . then

95

100

x =

95 110

100

x = Rs. 11010

69. (*) Initial expenditure of Krishnamurthy

=80

15000100

= Rs. 12000

New income

=15000 120

100

= Rs. 18000

New expenditure

=12000 120

100

= Rs. 14400

New savings = 18000 14400

= Rs. 3600

Note: It is not an answer choice.

70. First number

=25

1002

=225

2

Second number = 125

Required percentage

=225

1002 125

= 90

71. Percentage of increase

=2 22 2 %100

= 4.04%

72. Percentage of students opting for bothsubjects

= 72 + 44 100 = 16

If the total number of students bex, then

16

100

x = 40 x =

4000

16= 250

73. A : B + C = 2 : 5

As share =

21050

7

= Rs. 30075. Numbers = 5x and 6x

HCF = x = 4

LCM = 5 6 x

= 5 6 4 = 120

76. a + b + c = 1,

ab + bc + ca =1

3

a2 + b2 + c2

= (a + b + c)2 2 (ab + bc + ca)

= 213

= 13

Clearly, a = b = c =1

3

a : b : c = 1 : 1 : 1

77. If B invested fory months. then

5 8

6 y

=

5

9

y = 12 months.

79. l2 + b2 = 625 ...(i)

lb = 168 ...(ii)

(l + b)2 = l2 + b2 + 2lb

= 625 + 2 168 = 961


16/17

Solved Paper

16

l + b = 961 = 31 ...(iii)

(l + b)2 = l2 + b2 2lb= 625 168 2 = 289

l b = 289 = 17 ...(iv)

From equations (iii) and (iv),

2l = 48

l =48

2= 24 cm

80. Volume of the cylinder = r2h

= 32 8 = 72 cm3

Volume of one coin

= (0.75)2 0.2 Number of coins

=72

0.75 0.75 0.2

= 640

81. 4 (r + 2)2 4 r2 = 704

(r + 2)2 r2 =704

4

r2 + 4r + 4 r2

=704 7

4 22

= 56

4r = 56 4 = 52

r = 13 metre

82. Required ratio = Volume of hemi-sphere :Volume of cyliner

=32

3r : r3 = 2 : 3

84. T = 2 half years

Rate = 6%

= CI =2

P 1 1100

r

=2

66250 1 1

100

= 6250 0.1236 = Rs. 772.5

85. 1460 =2

P 1100

R

...(i)

1606 =

3

P 1100

R

...(ii)

Dividing equation (ii) by (i)

1100

R =

1606

1460

R

100=

1606 1460

1460

=146

1460=

1

10

86. If the distance between the school and homebe x km, then

3 4

x x =

10

60

12

x=

1

6

x =1

126

= 2 km

87. 60 kmph =60 5

m/sec

18

=50

m/sec3

If the speed of second train be x m/sec, then

50

3x =

120

18=

20

3

x =50 20

3 3 = 10 m/sec

=10 18

kmph

5

= 36 kmph

89. 8 4m + 6w 8

10 3m + 7 10w


17/17

Solved Paper

17

2m 22w

1m 11w 4m + 6w = 50w

M1D1 = M2D2 50 8 = 20 D2

D2 =50 8

20

= 20 days

90. A + B = 40

B + C = 38

C + A = 42

On adding,

2(A + B + C) = 40 + 38 + 42 = 120

A + B + C = 60

A = (A + B + C) (B + C)

= 60 38 = 22

91. Expenditure on housing and transport

=10

150000100

= Rs. 15000

92. It is obvious from the pie chart.

Food 23%, Others 20%

93. Housing 15%

Savings 15%

94. Required percentage

= 10 + 12 + 5= 27%

95. Expenditure on food

=150000 23

Rs.100

= Rs. 34500

96. Required percentage

=300

1001200

= 25

97. Number of persons killed in 2009

= 800 + 200 = 100098. It is obvious from the bar diagram.

Required number of the dead = 1200

99. It is obvious from the bar diagram.

Required number of the dead = 150

100. Required average

=1500 1050 1300 1000

4

=4850

4= 1212.5
http://www.upscportal.com/

Documents

Ssc Cgl Tier II Solved Paper