Mental maths ix q & a

APTITUDE:

Time and Work

1. A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the

fraction of the work that is left is :

A.

1

4

B.

1

10

C.

7

15

D.

8

15

Answer: Option D

Explanation:

A's 1 day's work = 1

; 15

B's 1 day's work = 1

; 20

(A + B)'s 1 day's work = 1

+ 1

= 7 .

15 20 60

(A + B)'s 4 day's work = 7

x 4 = 7 .

60 15

Therefore, Remaining work = 1 - 7

= 8 .

15 15

2. A can lay railway track between two given stations in 16 days and B can do the same job in

12 days. With help of C, they did the job in 4 days only. Then, C alone can do the job in:

A. 91

days 5

B. 92

days 5

C. 93

days 5

D. 10

Answer: Option C

Explanation:(A + B + C)'s 1 day's work = 1

, 4

A's 1 day's work = 1

, 16

B's 1 day's work = 1

. 12

C's 1 day's work = 1

- 1

+ 1

= 1

- 7

= 5 .

4 16 12 4 48 48

So, C alone can do the work in 48

= 9 3

days. 5 5

3. A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C

together can do it in 2 hours. How long will B alone take to do it?

A. 8 hours B. 10 hours

C. 12 hours D. 24 hours

Answer: Option C

Explanation:

A's 1 hour's work = 1

; 4

(B + C)'s 1 hour's work = 1

; 3

(A + C)'s 1 hour's work = 1

. 2

(A + B + C)'s 1 hour's work = 1

+ 1

= 7 .

4 3 12

B's 1 hour's work = 7

- 1

= 1 .

12 2 12

B alone will take 12 hours to do the work.

4. If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the

same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will

be:

A. 4 days B. 5 days

C. 6 days D. 7 days

Answer: Option A

Explanation:

Let 1 man's 1 day's work = x and 1 boy's 1 day's work = y.

Then, 6x + 8y = 1

and 26x + 48y = 1.

10 2

Solving these two equations, we get : x = 1

and y = 1

.100 200

(15 men + 20 boy)'s 1 day's work = 15

+ 20

= 1.

100 200 4

15 men and 20 boys can do the work in 4 days.

--------------------------------------------------------

Time and Distance

5. An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the

same distance in 1 hours, it must travel at a speed of:

A. 300 kmph B. 360 kmph

C. 600 kmph D. 720 kmph

Answer: Option D

Explanation:

Distance = (240 x 5) = 1200 km.

Speed = Distance/Time

Speed = 1200/(5/3) km/hr. [We can write 1 hours as 5/3 hours]

Required speed = 1200 x 3

km/hr= 720 km/hr.

5

6. If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The

actual distance travelled by him is:

A. 50 km B. 56 km

C. 70 km D. 80 km

Answer: Option A

Explanation:

Let the actual distance travelled be x km.

Then, x

= x + 20

10 14

14x = 10x + 200

4x = 200

x = 50 km.

Simple Interest

7. A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is

the rate of interest?

A. 3% B. 4%

C. 5% D. 6%

E. None of these

Answer: Option D

Explanation:

S.I. = Rs. (15500 - 12500) = Rs. 3000.

Rate =

100 x 3000

% = 6%

12500 x 4

8. A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years.

The sum is:

A. Rs. 650 B. Rs. 690

C. Rs. 698 D. Rs. 700

Answer: Option C

Explanation:

S.I. for 1 year = Rs. (854 - 815) = Rs. 39.

S.I. for 3 years = Rs.(39 x 3) = Rs. 117.

Principal = Rs. (815 - 117) = Rs. 698.

9. A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to

pay Rs. 5400 interest only for the period. The principal amount borrowed by him was:

A. Rs. 2000 B. Rs. 10,000

C. Rs. 15,000 D. Rs. 20,000

Answer: Option C

Explanation:

Principal = Rs. 100 x 5400

= Rs. 15000. 12 x 3

10. What will be the ratio of simple interest earned by certain amount at the same rate of

interest for 6 years and that for 9 years?

A. 1 : 3 B. 1 : 4

C. 2 : 3 D. Data inadequate

E. None of these

Answer: Option C

Explanation:

Let the principal be P and rate of interest be R%.

Required ratio =

P x R x 6

100 =

6PR=

6= 2 : 3.

P x R x 9

100

9PR 9

Profit and Loss

11. Alfred buys an old scooter for Rs. 4700 and spends Rs. 800 on its repairs. If he sells the

scooter for Rs. 5800, his gain percent is:

A. 44%

7

B. 55 %

11

C. 10% D. 12%

Answer: Option B

Explanation:

Cost Price (C.P.) = Rs. (4700 + 800) = Rs. 5500.

Selling Price (S.P.) = Rs. 5800.

Gain = (S.P.) - (C.P.) = Rs.(5800 - 5500) = Rs. 300.

Gain % = 300

x 100 %

= 55 %

5500 11

12. If selling price is doubled, the profit triples. Find the profit percent.

Answer: Option B

Explanation:

Let C.P. be Rs. x and S.P. be Rs. y.

Then, 3(y - x) = (2y - x) y = 2x.

Profit = Rs. (y - x) = Rs. (2x - x) = Rs. x.

Profit % = x

x 100 % = 100%x

13. A vendor bought toffees at 6 for a rupee. How many for a rupee must he sell to gain 20%?

A. 3 B. 4

C. 5 D. 6

Answer: Option C

Explanation:

C.P. of 6 toffees = Re. 1

S.P. of 6 toffees = 120% of Re. 1 = Rs. 6

5

For Rs. 6

, toffees sold = 6. 5

For Re. 1, toffees sold = 6 x 5

= 5. 6

14. A man buys a cycle for Rs. 1400 and sells it at a loss of 15%. What is the selling price of the

cycle?

A. Rs. 1090 B. Rs. 1160

C. Rs. 1190 D. Rs. 1202

Answer: Option C

Explanation:

S.P. = 85% of Rs. 1400 = Rs. 85

x 1400 = Rs. 1190 100

Percentage

15. A batsman scored 110 runs which included 3 boundaries and 8 sixes. What percent of his

total score did he make by running between the wickets?

A. 45% B. 455 %

11

C. 546 %

11

D. 55%

Answer: Option B

Explanation:

Number of runs made by running = 110 - (3 x 4 + 8 x 6)

= 110 - (60)

= 50.

Required percentage = 50

x 100% = 45

5 %

110 11

16. If 20% of a = b, then b% of 20 is the same as:

A. 4% of a B. 5% of a

C. 20% of a D. None of these

Answer: Option A

Explanation:

20% of a = b 20

a = b. 100

b% of 20 = b

x 20 =

20 a x

1 x 20 =

4 a = 4% of a.

100 100 100 100

17. In an election between two candidates, one got 55% of the total valid votes, 20% of the

votes were invalid. If the total number of votes was 7500, the number of valid votes that the

other candidate got, was:

A. 2700 B. 2900

C. 3000 D. 3100

Answer: Option A

Explanation:

Number of valid votes = 80% of 7500 = 6000.

Valid votes polled by other candidate = 45% of 6000

= 45

x 6000 = 2700. 100

18. Three candidates contested an election and received 1136, 7636 and 11628 votes

respectively. What percentage of the total votes did the winning candidate get?

A. 57% B. 60%

C. 65% D. 90%

Answer: Option A

Explanation:

Total number of votes polled = (1136 + 7636 + 11628) = 20400.

Required percentage = 11628

x 100% = 57%.20400

19. The population of a town increased from 1,75,000 to 2,62,500 in a decade. The average

percent increase of population per year is:

A. 4.37% B. 5%

C. 6% D. 8.75%

Answer: Option B

Explanation:

Increase in 10 years = (262500 - 175000) = 87500.

Increase% = 87500

x 100 % = 50%.175000

Required average = 50

% = 5%.10

Average

20. In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate

in the remaining 40 overs to reach the target of 282 runs?

A. 6.25 B. 6.5

C. 6.75 D. 7

Answer: Option A

Explanation:

Required run rate = 282 - (3.2 x 10)

= 250

= 6.25 40 40

21. A family consists of two grandparents, two parents and three grandchildren. The average

age of the grandparents is 67 years, that of the parents is 35 years and that of the

grandchildren is 6 years. What is the average age of the family?

A. 28 4

years7

B. 31 5

years7

C. 32 1

years7

D. None of these

Answer: Option B

Explanation:

Required average

=

67 x 2 +

35 x 2 + 6

x 3

2 + 2 + 3

=

134 + 70

+ 18

7

= 222

7

= 31 5 years.

7

22. A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5

consecutive months. How much sale must he have in the sixth month so

that he gets an average sale of Rs. 6500?

A. Rs. 4991 B. Rs. 5991

C. Rs. 6001 D. Rs. 6991

Answer: Option A

Explanation:

Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.

Required sale = Rs. [ (6500 x 6) - 34009 ]

= Rs. (39000 - 34009)

= Rs. 4991.

23. he average weight of 8 person's increases by 2.5 kg when a new person comes in place of

one of them weighing 65 kg. What might be the weight of the new person?

A. 76 kg B. 76.5 kg

C. 85 kg D. Data inadequate

E. None of these

Answer: Option C

Explanation:

Total weight increased = (8 x 2.5) kg = 20 kg.

Weight of new person = (65 + 20) kg = 85 kg.

24. The average age of husband, wife and their child 3 years ago was 27 years and that of wife

and the child 5 years ago was 20 years. The present age of the husband is:

A. 35 years B. 40 years

C. 50 years D. None of these

Answer: Option B

Explanation:

Sum of the present ages of husband, wife and child = (27 x 3 + 3 x 3) years = 90 years.

Sum of the present ages of wife and child = (20 x 2 + 5 x 2) years = 50 years.

Husband's present age = (90 - 50) years = 40 years.

25. The average weight of 16 boys in a class is 50.25 kg and that of the remaining 8 boys is

45.15 kg. Find the average weights of all the boys in the class.

A. 47.55 kg B. 48 kg

C. 48.55 kg D. 49.25 kg

Answer: Option C

Explanation:

Required average

= 50.25 x 16 + 45.15 x 8

16 + 8

= 804 + 361.20

24

= 1165.20

24

= 48.55

26. If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60,

then the average marks of all the students is:

A. 53.33 B. 54.68

C. 55 D. None of these

Answer: Option B

Explanation:

Required average

= 55 x 50 + 60 x 55 + 45 x 60

55 + 60 + 45

= 2750 + 3300 + 2700

160

= 8750

160

Decimal Fraction

27. Evaluate : (2.39)2 - (1.61)2

2.39 - 1.61

A. 2 B. 4

C. 6 D. 8

Answer: Option B

Explanation:

Given Expression = a2 - b2

= (a + b)(a - b)

= (a + b) = (2.39 + 1.61) = 4. a - b (a - b)

28. What decimal of an hour is a second ?

A. .0025 B. .0256

C. .00027 D. .000126

Answer: Option C

Explanation:

Required decimal = 1

= 1

= .00027 60 x 60 3600

29. The value of 0.1 x 0.1 x 0.1 + 0.02 x 0.02 x 0.02

is:0.2 x 0.2 x 0.2 + 0.04 x 0.04 x 0.04

A. 0.0125 B. 0.125

C. 0.25 D. 0.5

Answer: Option B

Explanation:

Given expression = (0.1)3 + (0.02)3

= 1

= 0.125 23 [(0.1)3 + (0.02)3] 8

30.

4.2 x 4.2 - 1.9 x 1.9 is equal to:

2.3 x 6.1

A. 0.5 B. 1.0

C. 20 D. 22

Answer: Option B

Explanation:

Given Expression = (a2 - b2)

= (a2 - b2)

= 1. (a + b)(a - b) (a2 - b2)

31. If 144

= 14.4

, then the value of x is: 0.144 x

A. 0.0144 B. 1.44

C. 14.4 D. 144

Answer: Option A

Explanation:

144 =

14.4

0.144 x

144 x 1000=

14.4

144 x

x = 14.4

= 0.0144 1000

LOGICAL REASONING:

Number Series

32. Look at this series: 2, 1, (1/2), (1/4), ... What number should come next?

A. (1/3) B. (1/8)

C. (2/8) D. (1/16)

Answer: Option B

Explanation:

This is a simple division series; each number is one-half of the previous number.

In other terms to say, the number is divided by 2 successively to get the next result.

4/2 = 2

2/2 = 1

1/2 = 1/2

(1/2)/2 = 1/4

(1/4)/2 = 1/8 and so on.

33. Look at this series: 58, 52, 46, 40, 34, ... What number should come next?

A. 26 B. 28

C. 30 D. 32

Answer: Option B

Explanation:

This is a simple subtraction series. Each number is 6 less than the previous number.

34. Look at this series: 3, 4, 7, 8, 11, 12, ... What number should come next?

A. 7 B. 10

C. 14 D. 15

Answer: Option D

Explanation:

This alternating addition series begins with 3; then 1 is added to give 4; then 3 is added to give 7;

then 1 is added, and so on.

35. Look at this series: 31, 29, 24, 22, 17, ... What number should come next?

A. 15 B. 14

C. 13 D. 12

Answer: Option A

Explanation:

This is a simple alternating subtraction series, which subtracts 2, then 5.

DATA INTERPRETATION

36. Bar Charts

1. What is the average sales of all the branches (in thousand numbers) for the year 2000?

A. 73 B. 80

C. 83 D. 88

Answer: Option B

Explanation:

Average sales of all the six branches (in thousand numbers) for the year 2000

= 1

x [80 + 75 + 95 + 85 + 75 + 70]6

= 80.

2. Total sales of branches B1, B3 and B5 together for both the years (in thousand numbers) is?

A. 250 B. 310

C. 435 D. 560

Answer: Option D

Explanation:

Total sales of branches B1, B3 and B5 for both the years (in thousand numbers)

= (80 + 105) + (95 + 110) + (75 + 95)

= 560.

3. What is the ratio of the total sales of branch B2 for both years to the total sales of branch B4

for both years?

A. 2:3 B. 3:5

C. 4:5 D. 7:9

Answer: Option D

Explanation:

Required ratio = (75 + 65)

= 140

= 7.

(85 + 95) 180 9

NON VERBAL REASONING

Series

37. Select a figure from amongst the Answer Figures which will continue the same series as

established by the five Problem Figures.

Problem Figures: Answer Figures:

(A) (B) (C) (D) (E) (1) (2) (3) (4) (5)

A. 1 B. 2

C. 3 D. 4

E. 5

Answer: Option A

Explanation:

In each step, the dot moves one space CW and the arrow moves two spaces CW.




(A) (B) (C) (D) (E) (1) (2) (3) (4) (5)

A. 1 B. 2

C. 3 D. 4

E. 5

Answer: Option C

Explanation:

The pin rotates 45oCW and 90oCW alternately and moves one space (each space is equal to half-a-

side of the square) and two spaces CW alternately. The arrow rotates 90oACW and 45oACW

alternately and moves two spaces and one space.




(A) (B) (C) (D) (E) (1) (2) (3) (4) (5)

A. 1 B. 2

C. 3 D. 4

E. 5

Answer: Option C

Explanation:

In each step, the pin rotates 90oCW and the arrow rotates 90oACW.




(A) (B) (C) (D) (E) (1) (2) (3) (4) (5)

A. 1 B. 2

C. 3 D. 4

E. 5

Answer: Option D

Explanation:

In each step, all the elements move to the adjacent corner (of the square boundary) in a CW

direction and the element that reaches the upper-left corner gets vertically inverted.




(A) (B) (C) (D) (E) (1) (2) (3) (4) (5)

A. 1 B. 2

C. 3 D. 4

E. 5

Answer: Option D

Explanation:

In each step, the first element moves to the third position and gets replaced by a new element; the

second and the third elements move to the first and the second positions respectively and the

entire figure rotates 90oCW.

Analytical Reasoning

41. Find the number of triangles in the given figure.

A. 8 B. 10

C. 12 D. 14

Answer: Option D

Explanation:

42. The figure may be labelled as shown.

The simplest triangles are AHG, AIG, AIB, JFE, CJE and CED i.e. 6 in number.

The triangles composed of two components each are ABG, CFE, ACJ and EGI i.e. 4 in number.

The triangles composed of three components each are ACE, AGE and CFD i.e. 3 in number.

There is only one triangle i.e. AHE composed of four components.

Therefore, There are 6 + 4 + 3 + 1 = 14 triangles in the given figure.

42. Find the minimum number of straight lines required to make the given figure.

A. 13 B. 15

C. 17 D. 19

Answer: Option A

Explanation:

The figure may be labelled as shown.

The horizontal lines are IJ, AB, EF, MN, HG, DC and LK i.e. 7 in number.

The vertical lines are AD, EH, IL, FG, BC and JK i.e. 6 in number.

Thus, there are 7 + 6 = 13 straight lines in the figure.

43. Find the number of triangles in the given figure.

A. 4 B. 5

C. 6 D. 7

Answer: Option B

Explanation:

The figure may be labelled as shown.

The simplest triangles are ADE, BDF, DEF and EFC i.e. 4 in number.

There is only one triangle ABC composed of four components.

Thus, there are 4+1 = 5 triangles in the given figure.

Mirror Images

VERBAL REASONING

Series Completion

44. 120, 99, 80, 63, 48, ?

A. 35 B. 38

C. 39 D. 40

Answer: Option A

Explanation:

The pattern is - 21, - 19, - 17, - 15,.....

So, missing term = 48 - 13 = 35.

45. 3, 10, 101,?

A. 10101 B. 10201

C. 10202 D. 11012

Answer: Option C

Explanation:

Each term in the series is obtained by adding 1 to the square of the preceding term.

So, missing term = (101)2 + 1 = 10202.

46. 125,80,45,20,?

A. 5 B. 8

C. 10 D. 12

Answer: Option A

Explanation:

The pattern is - 45, - 35, - 25, .....

So, missing term = 20 - 15 = 5.

Seating Arrangement

47. A, P, R, X, S and Z are sitting in a row. S and Z are in the centre. A and P are at the ends. R is

sitting to the left of A. Who is to the right of P ?

A. A B. X

C. S D. Z

Answer: Option B

Explanation:

The seating arrangement is as follows:

Therefore, right of P is X.

48. A, B, C, D and E are sitting on a bench. A is sitting next to B, C is sitting next to D, D is not sitting

with E who is on the left end of the bench. C is on the second position from the right. A is to the

right of B and E. A and C are sitting together. In which position A is sitting ?

A. Between B and D B. Between B and C

C. Between E and D D. Between C and E

Answer: Option B

Explanation:

Therefore, A is sitting in between B and C.

49. Which one is immediate right to the V ?

A. P B. U

C. R D. T

Answer: Option D

Explanation:

T is immediate right to the V.

50. Who is sitting immediate right to Reeta ?

A. Bindu B. Rani

C. Mary D. Seema

Answer: Option C

Explanation:

Mary is sitting immediate right to Reeta.

DATA INT

51. Study the following table and answer the questions based on it.

Expenditures of a Company (in Lakh Rupees) per Annum Over the given Years.

Year

Item of Expenditure

Salary Fuel and Transport Bonus Interest on Loans Taxes

1998 288 98 3.00 23.4 83

1999 342 112 2.52 32.5 108

2000 324 101 3.84 41.6 74

2001 336 133 3.68 36.4 88

2002 420 142 3.96 49.4 98

1. What is the average amount of interest per year which the company had to pay during this

period?

A. Rs. 32.43 lakhs B. Rs. 33.72 lakhs

C. Rs. 34.18 lakhs D. Rs. 36.66 lakhs

2. What is the average amount of interest per year which the company had to pay during this

period?



Answer: Option D

Explanation:

Average amount of interest paid by the Company during the given period

= Rs. 23.4 + 32.5 + 41.6 + 36.4 + 49.4

lakhs 5

= Rs. 183.3

lakhs 5

= Rs. 36.66 lakhs.

2. The total amount of bonus paid by the company during the given period is approximately what

percent of the total amount of salary paid during this period?

A. 0.1% B. 0.5%

C. 1% D. 1.25%

Answer: Option C

Explanation:

Required percentage = (3.00 + 2.52 + 3.84 + 3.68 + 3.96)

x 100 % (288 + 342 + 324 + 336 + 420)

= 17

x 100 %1710

1%.

3. Total expenditure on all these items in 1998 was approximately what percent of the total

expenditure in 2002?

A. 62% B. 66%

C. 69% D. 71%

Answer: Option C

Explanation:

Required percentage = (288 + 98 + 3.00 + 23.4 + 83) x 100 %

(420 + 142 + 3.96 + 49.4 + 98)

= 495.4

x 100 %713.36

69.45%.

4. The total expenditure of the company over these items during the year 2000 is?



Answer: Option A

Explanation:

Total expenditure of the Company during 2000

= Rs. (324 + 101 + 3.84 + 41.6 + 74) lakhs

= Rs. 544.44 lakhs.

5. The ratio between the total expenditure on Taxes for all the years and the total expenditure on

Fuel and Transport for all the years respectively is approximately?

A. 4:7 B. 10:13

C. 15:18 D. 5:8

Answer: Option B

Explanation:

Required ratio = (83 + 108 + 74 + 88 + 98)

(98 + 112 + 101 + 133 + 142)

= 451

586

=

1

1.3

= 10

.13

52. Study the following table and answer the questions.

Number of Candidates Appeared and Qualified in a Competitive Examination from Different States

Over the Years.

State

Year

1997 1998 1999 2000 2001

App. Qual. App. Qual. App. Qual. App. Qual. App. Qual.

M 5200 720 8500 980 7400 850 6800 775 9500 1125

N 7500 840 9200 1050 8450 920 9200 980 8800 1020

P 6400 780 8800 1020 7800 890 8750 1010 9750 1250

Q 8100 950 9500 1240 8700 980 9700 1200 8950 995

R 7800 870 7600 940 9800 1350 7600 945 7990 885

Total number of candidates qualified from all the states together in 1997 is approximately what

percentage of the total number of candidates qualified from all the states together in 1998?

A. 72% B. 77%

C. 80% D. 83%

Answer: Option C

Explanation:

Required percentage = (720 + 840 + 780 + 950 + 870)

x 100 % (980 + 1050 + 1020 + 1240 + 940)

=

4160x 100 %

5230

= 79.54% 80%.

What is the average candidates who appeared from State Q during the given years?

A. 8700 B. 8760

C. 8990 D. 8920

Answer: Option C

Explanation:

Required average = 8100 + 9500 + 8700 + 9700 + 8950

5

= 44950

5

= 8990.

In which of the given years the number of candidates appeared from State P has maximum percentage

of qualified candidates?

A. 1997 B. 1998

C. 1999 D. 2001

Answer: Option D

Explanation:

The percentages of candidates qualified to candidates appeared from State P during different years

are:

For 1997 780

x 100 % = 12.19%.6400

For 1998 1020

x 100 % = 11.59%.8800

For 1999 890

x 100 % = 11.41%.7800

For 2000 1010

x 100 % = 11.54%.8750

For 2001 1250

x 100 % = 12.82%.9750

Maximum percentage is for the year 2001.

What is the percentage of candidates qualified from State N for all the years together, over the

candidates appeared from State N during all the years together?

A. 12.36% B. 12.16%

C. 11.47% D. 11.15%

Answer: Option D

Explanation:


x 100 % (7500 + 9200 + 8450 + 9200 + 8800)

= 4810

x 100 %43150

= 11.15%

The percentage of total number of qualified candidates to the total number of appeared candidates

among all the five states in 1999 is?

A. 11.49% B. 11.84%

C. 12.21% D. 12.57%

Answer: Option B

Explanation:


x 100 %(7400 + 8450 + 7800 + 8700 + 9800)

= 4990

x 100 %42150

= 11.84%.

53. The following table gives the percentage of marks obtained by seven students in six different

subjects in an examination.

The Numbers in the Brackets give the Maximum Marks in Each Subject.

Student

Subject (Max. Marks)

Maths Chemistry Physics Geography History Computer

Science

(150) (130) (120) (100) (60) (40)

Ayush 90 50 90 60 70 80

Aman 100 80 80 40 80 70

Sajal 90 60 70 70 90 70

Rohit 80 65 80 80 60 60

Muskan 80 65 85 95 50 90

Tanvi 70 75 65 85 40 60

Tarun 65 35 50 77 80 80

What are the average marks obtained by all the seven students in Physics? (rounded off to two digit

after decimal)

A. 77.26 B. 89.14

C. 91.37 D. 96.11

Answer: Option B

Explanation:

Average marks obtained in Physics by all the seven students

= 1

x [ (90% of 120) + (80% of 120) + (70% of 120)7

+ (80% of 120) + (85% of 120) + (65% of 120) + (50% of 120) ]

= 1 x [ (90 + 80 + 70 + 80 + 85 + 65 + 50)% of 120 ]

7

= 1

x [ 520% of 120 ] 7

= 624

7

= 89.14.

The number of students who obtained 60% and above marks in all subjects is?

A. 1 B. 2

C. 3 D. None

Answer: Option B

Explanation:

From the table it is clear that Sajal and Rohit have 60% or more marks in each of the six subjects.

What was the aggregate of marks obtained by Sajal in all the six subjects?

A. 409 B. 419

C. 429 D. 449

Answer: Option D

Explanation:

Aggregate marks obtained by Sajal

= [ (90% of 150) + (60% of 130) + (70% of 120)

+ (70% of 100) + (90% of 60) + (70% of 40) ]

= [ 135 + 78 + 84 + 70 + 54 + 28 ]

= 449.

In which subject is the overall percentage the best?

A. Maths B. Chemistry

C. Physics D. History

Answer: Option A

Explanation:

We shall find the overall percentage (for all the seven students) with respect to each subject.

The overall percentage for any subject is equal to the average of percentages obtained by all the

seven students since the maximum marks for any subject is the same for all the students.

Therefore, overall percentage for:

(i) Maths = 1

x (90 + 100 + 90 + 80 + 80 + 70 + 65) %7

= 1

x (575) %7

= 82.14%.

(ii) Chemistry = 1

x (50 + 80 + 60 + 65 + 65 + 75 + 35) %7

= 1

x (430) %7

= 61.43%.

(iii) Physics = 1

x (90 + 80 + 70 + 80 + 85 + 65 + 50) %7

= 1

x (520) %7

= 74.29%.

(iv) Geography = 1

x (60 + 40 + 70 + 80 + 95 + 85 + 77) %7

=

1x (507) %

7

= 72.43%.

(v) History = 1

x (70 + 80 + 90 + 60 + 50 + 40 + 80) %7

= 1

x (470) %7

= 67.14%.

(vi) Comp. Science = 1

x (80 + 70 + 70 + 60 + 90 + 60 + 80) %7

= 1

x (510) %7

= 72.86%.

Clearly, this percentage is highest for Maths.

What is the overall percentage of Tarun?

A. 52.5% B. 55%

C. 60% D. 63%

Answer: Option C

Explanation:

Aggregate marks obtained by Tarun

= [ (65% of 150) + (35% of 130) + (50% of 120)

+ ((77% of 100) + (80% of 60) + (80% of 40) ]

= [ 97.5 + 45.5 + 60 + 77 + 48 + 32 ]

= 360.

The maximum marks (of all the six subjects)

= (150 + 130 + 120 + 100 + 60 + 40)

= 600.

Overall percentage of Tarun = 360

x 100 % = 60%.600

PERCENTAGE:

54. A student multiplied a number by 3

instead of 5

. 5 3

What is the percentage error in the calculation?

A. 34% B. 44%

C. 54% D. 64%

Answer: Option D

Explanation:

Let the number be x.

Then, error = 5x -

3x =

16x.

3 5 15

Error% =

16x x

3 x 100

% = 64%. 15 5x 55. Two tailors X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of

the sum paid to Y, how much is Y paid per week?

A. Rs. 200 B. Rs. 250

C. Rs. 300 D. None of these

Answer: Option B

Explanation:

Let the sum paid to Y per week be Rs. z.

Then, z + 120% of z = 550.

z + 120

z = 550 100

11z = 550

5

z =

550 x 5

= 250. 11

56. Gauri went to the stationers and bought things worth Rs. 25, out of which 30 paise went on sales tax

on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?

A. Rs. 15 B. Rs. 15.70

C. Rs. 19.70 D. Rs. 20

Answer: Option C

Explanation:

Let the amount taxable purchases be Rs. x.

Then, 6% of x = 30

100

x = 30

x 100

= 5. 100 6

Cost of tax free items = Rs. [25 - (5 + 0.30)] = Rs. 19.70

57. Rajeev buys good worth Rs. 6650. He gets a rebate of 6% on it. After getting the rebate, he pays

sales tax @ 10%. Find the amount he will have to pay for the goods.

A. Rs. 6876.10 B. Rs. 6999.20

C. Rs. 6654 D. Rs. 7000

Answer: Option A

Explanation:

Rebate = 6% of Rs. 6650 = Rs. 6

x 6650 = Rs. 399. 100

Sales tax = 10% of Rs. (6650 - 399) = Rs. 10

x 6251 = Rs. 625.10 100

Final amount = Rs. (6251 + 625.10) = Rs. 6876.10

----------------------

58. The ages of the two persons differ by 20 years. If 5 year ago, the older one be 5 times as old

as the younger one, then their present ages, in year are:

A. 25, 5,

B. 30, 10

C. 35, 15

D. 50, 30

59. In what ratio must rice at Rs 9.30 per Kg be mixed with rice at Rs 10.80 per Kg so that the

mixture be worth Rs 10 per Kg?

A. 6:5

B. 8:7

C. 3:7

D. 6:1

Answer – (B)

Solution:

C.P of 1 Kg C.P of 1 Kg

rice of 1st rice of 2nd

kind (930p) kind (1080p)

\ /

Mean Price

(1000p)

/ \

(1080 – 1000) : (1000 - 930)

80 70

Thus, required ratio = 80 : 70 = 8 : 7

60. How much water must be added to 60 litres of milk at 1.5 litres for Rs. 20 So as to have a

mixture worth Rs.10 2/3 a litre?

A. 10 litres

B. 12 litres

C. 15 litres

✖ D. 18 litres

Answer – (C)

Solution:

C.P. of 1 litre of milk =Rs.

(20x2)

3

=Rs.

40

3

C.P. of 1 litre of water = 0

Mean price = Rs.

32

3

By the rule of alligation, we have:

C.P of 1 litre C.P of 1 litre

Of water of milk

(0) (Rs. 40/3)

\ /

Mean Price

(Rs. 32/3)

/ \

(

40

3

–

32

3

) (

32

3−0

)

8/3 32/3

Ratio of water and milk =

8

3

:

32

3

=8:32=1:4

Thus, Quantity of water to be added to 60 litres of milk = (

1

4

×60)litres= 15 litres

61. In what ratio must wheat at Rs.3.20 per kg be mixed with wheat at Rs.2.90 per kg so that the

mixture be worth Rs.3.08 per kg?

A. 3 : 4

B. 2 : 3

C. 3 : 2

✖ D. 4 : 3

Answer – (C)

Solution:

C.P of a unit quantity of 1st kind = Rs. 3.20

C.P of a unit quantity of 2nd kind = Rs. 2.90

Mean price = Rs.3.08

C.P of unit quantity C.P of unit quantity

of 1st kind of 2nd kind

(Rs. 3.20) (Rs. 2.90)

\ /

Mean Price

(Rs.3.08)

/ \

(3.08 – 2.90) : (3.20 – 3.08)

0.18 0.12

Required ratio = 0.18 : 0.12 = 3 : 2

62. In what proportion must rice at Rs. 3.10 per kg be mixed with rice at Rs. 3.60 per kg so that

the mixture be worth Rs. 3.25 per kg?

A. 3 : 7

B. 5 : 3

C. 3 : 5

✔ D. 7 : 3

Answer – (D)

Solution:

C.P of a unit quantity of 1st kind = 310p (in paise)

C.P of a unit quantity of 2nd kind = 360p

Mean price = 325p

C.P of unit quantity C.P of unit quantity

of 1st kind of 2nd kind

(310p) (360p)

\ /

Mean Price

(325p)

/ \

(360 – 325) : (325 – 310)

35 15

Required ratio = 35 : 15 = 7 : 3

They must be mixed in the ratio 7 : 3

AVERAGE:

68. The average of first five multiples of 3 is :

A. 9

B. 10

C. 8

✖ D. 11

Answer – (A)

Solution:

Basic Formula:

1, 2, 3 ..⋯ n

If n is odd, the formula is (

n+1

2

)th term

The five multiples of 3 is 3, 6, 9, 12, 15

(

n+1

2

) ⇒ (

5+1

2

)th term

⇒

6

2

th term =3rd term

Here 3rd term is 9

69. There are two sections A and B of a class, consisting of 36 and 44 students’ respectively. If

the average weight of section A is 40kg and that of section B is 35kg, find the average weight of

the whole class.

A. 30 kg

B. 35 kg

C. 42.5 kg

D. 37.25 kg

Answer – (D)

Solution:

Total weight of (36+44) Students = (36x40+44x35)kg = 2980kg

Therefore average weight of the whole class = (2980/80) kg

Therefore average weight = 37.25kg

Distance between two stations A and B is 778km. A train covers the journey from A to B at

84km per hour and returns back to A with a uniform speed of 56km per hour. Find the average

speed of train during the whole journey.

A. 60 km/hr

B. 30.5 km/hr

C. 57 km/hr

✔ D. 67.2 km/hr

Answer - (D)

Solution:

Average speed=(

2xy

x+y

)km/hr

=(

2×84×56

84+56

) km/hr

=(

2×84×56

140

)km/hr

= 67.2km/hr.

APTITUDE:

Exam2win > Aptitude Question Papers (All Topics)

APTITUDE QUESTIONS AND ANSWERS 1 to 10

70. 1. A man lends Rs. 10000 in four parts. If be gets 8% on Rs. 2000 7 on Rs. 4000 and 8 on Rs. 1400

what per cent must he get for the remainder, if the average interest is 8.13%?

7%

9%

9

10

ANSWER : 9%

71. On july 2, 1985 it was Wednesday. The day of the week on July 2, 1984 was:

Wednesday

Tuesday

Monday

Thursday

ANSWER : Monday

72. A tank can be filled by one tap in 20 min, and by another in 25 min. both the taps are kept open

for 5 min, and then the second is turned off. In how many minutes more is the tank completely filled?

17 min

12 min

11 min

6 min

ANSWER : 1 min

73. If each side of a cube is doubled, then its volume :

is doubled

becomes 4 times

becomes 6 times

becomes 8 times

ANSWER : becomes 8 times

74. A sum of money is sufficient to pay A’s wages for 21 days or B’s wages for 28 days. The money

is sufficient to pay the wages of both for:

12 days

12 days

14 days

none of these

ANSWER : 12 days

75. The mean proportional between 0.32 and 0.02 is:

0.34

0.3

0.16

0.08

ANSWER : .08

76. The ratio of milk and water in 66 kg. of adulterated milk is 5 : 1. Water is added to it to make the

ratio 5 : 3. The quantity of water added is :

22 kg.

24.750 kg.

16.500 kg.

20 kg.

ANSWER : 22 kg.

77. The length of hall is 4/3) times its breadth. If the area of the hall be 300 square metres the

difference between the length and the breadth is:

15 metres

4 metres

3 metres

none of these

ANSWER : none of these

78. A can run a kilometer in 4 min. 54 sec. and B in 5 min. How many metres start can A give B in a

km race so that the race may end in a dead heat?

20 metres

16 metres

18 metres

14.5 metres

ANSWER : 20 metres

79. A,B,C, enter into a partnership and their capitals are in the proportion of . A withdraws half his

capital at the end of 4 months. Out of a total annual profit of Rs. 847, A’ share is:

Rs. 252

Rs. 280

Rs.315

Rs. 412

ANSWER : Rs. 280

AVERAGE


80. The average age of an adult class is 40 years. 12 new students with an average age of 32 years

join the class, thereby decreasing the average by 4 years. The original strength of the class was :

10

11

12

15

ANSWER : 12

81. A cistern is normally filled in 8 hours but takes two hours longer to fill because of a leak in it

sbottom. If the cistern is full, the leak will empty it in:

16 hrs

20 hrs

25 hrs

40 hrs

ANSWER : 0 hrs

82. The difference between simple interest and compound interest on a sum for 2 years at 8% when

the interest is compounded annually is Rs.16. If the interest were compounded half yearly, the

difference in two interests would be nearly:

Rs.16

Rs.16.80

Rs. 21.85

RS.24.64

ANSWER : RS.24.64

83. At what time between 9 and 10 will the hands of a watch be together ?

45 minutes past 9

50 minutes past 9

49 minutes past 9

48 minutes past 9

ANSWER : 49 minutes past 9

84. If I purchased 11 books for Rs. 10 and sold all the books at the rate of 10 books for Rs. 11, the

profit per cent is:

10%

11%

21%

100%

ANSWER : 21%

85. A fraction becomes 4 when 1 is added to the both the numerator and denominator; and it

becomes 7 when 1 is subtracted from both the numerator and denominator. The numerator of the

given fraction is:

2

3

7

15

ANSWER : 15

85. The current of a stream runs at 1 km/hr. A motor boat goes 35 km upstream and back again to

the starting point in 12 hours. The speed of motorboat in still water is :

6 km/hr

7 km/hr

8.5 km/hr

8 km/hr

ANSWER : 6 km/hr

86. A man sold 20 articles for Rs. 60 and gained 20%. How many articles did he buy for Rs.60?

22

24

25

26

ANSWER : 24

87. X an Y are two stations 500 km apart. A train starts form X and moves towards Y at 20 km/hr.

Another rain starts from Y at the same time and moves towards X at 30 km/hr. How far from X will

they cross each other:

200 km

300 km

120 km

40 km

ANSWER : 200 km

88. P.V. Narsimha Rao was elected party leader on 29 th may. 1991. What was the day of the week?

Tuesday

Friday

Wednesday

Sunday

ANSWER : Wednesday

AVERAGE


89. The average age of an adult class is 40 years. 12 new students with an average age of 32 years

join the class, thereby decreasing the average by 4 years. The original strength of the class was :

10

11

12

15

ANSWER : 12

90. A cistern is normally filled in 8 hours but takes two hours longer to fill because of a leak in it

sbottom. If the cistern is full, the leak will empty it in:

16 hrs

20 hrs

25 hrs

40 hrs

ANSWER : 0 hrs

91. The difference between simple interest and compound interest on a sum for 2 years at 8% when

the interest is compounded annually is Rs.16. If the interest were compounded half yearly, the

difference in two interests would be nearly:

Rs.16

Rs.16.80

Rs. 21.85

RS.24.64

ANSWER : RS.24.64

92. At what time between 9 and 10 will the hands of a watch be together ?

45 minutes past 9

50 minutes past 9

49 minutes past 9

48 minutes past 9

ANSWER : 49 minutes past 9

93. If I purchased 11 books for Rs. 10 and sold all the books at the rate of 10 books for Rs. 11, the

profit per cent is:

10%

11%

21%

100%

ANSWER : 21%

94. A fraction becomes 4 when 1 is added to the both the numerator and denominator; and it

becomes 7 when 1 is subtracted from both the numerator and denominator. The numerator of the

given fraction is:

2

3

7

15

ANSWER : 15

95. The current of a stream runs at 1 km/hr. A motor boat goes 35 km upstream and back again to

the starting point in 12 hours. The speed of motorboat in still water is :

6 km/hr

7 km/hr

8.5 km/hr

8 km/hr

ANSWER : 6 km/hr

96. A man sold 20 articles for Rs. 60 and gained 20%. How many articles did he buy for Rs.60?

22

24

25

26

ANSWER : 24

97. X an Y are two stations 500 km apart. A train starts form X and moves towards Y at 20 km/hr.

Another rain starts from Y at the same time and moves towards X at 30 km/hr. How far from X will

they cross each other:

200 km

300 km

120 km

40 km

ANSWER : 200 km

98. P.V. Narsimha Rao was elected party leader on 29 th may. 1991. What was the day of the week?

Tuesday

Friday

Wednesday

Sunday

ANSWER : Wednesday

VOLUME AND SURFACE AREA QUESTIONS AND ANSWERS 1 to 3

99. The length of diagonal of a cube is (14 x ) cm. The volume of the cube is :

2744 cm3

2744 cm3

588 cm3

3528 cm3

ANSWER : 2744 cm3

100. The surface area of a cuboid 22 cm by 12 cm by 7.5 cm, is :

1980 cm2

2076 cm2

1038 cm2

none of these

ANSWER : 1038 cm2

101. Given that 1 cubic cm of marble weight 25 gms, the weight of a marble block 28 cm in width

and 5 cm thick is 112 kg. the length of the block is :

36 cm

37.5 cm

32 cm

26.5 cm

ANSWER : 32 cm

PROBLEMS ON NUMBERS QUESTIONS AND ANSWERS 1 to 3

102. If one-fourth of one-third of one-half of a number is 15, the number is:

72

120

180

360

ANSWER : 360

103. Three numbers are in the ratio 3:4:5. The sum of the largest and the smallest equals the sum of

the third and 52. The smallest number is:

20

27

39

52

ANSWER : 39

104. The sum of three consecutive odd numbers is 57. The middle one is:

19

21

23

17

ANSWER : 19

PARTNERSHIP QUESTIONS AND ANSWERS 1 to 3

105. Jayant started a business, investing Rs. 6000. Six months later madhu joined him, investing Rs.

4000, If they made a profit of Rs. 5200 at the end of the year, how much must be the share of Madhu?

Rs. 2080

Rs.1300

Rs.1800

Rs. 2600

ANSWER : Rs.1800

106. A and B invest in business in the ratio 3 :2. If the 5% of the total profit goes to charity and A?s

share is Rs. 855, total profit is:

Rs.1576

Rs. 1537.50

Rs.1500

Rs.1425

ANSWER : Rs. 1500

107. A, B and c invest Rs. 2000, Rs.3000 and Rs. 4000 in a business, After one year, A removed his

money but B and C continued for one more year. If the net profit after 2 years be Rs.3200, them A?s

share in the Profit is:

Rs. 1000

Rs. 600

Rs. 800

Rs. 400

ANSWER : Rs. 400

108. Which of the following diagrams indicates the best relation between Travelers, Train and Bus ?

A.

B.

C.

D.

Answer & Explanation

Answer: Option C

Explanation:

Bus and Train are different from each other but some travelers travel by bus and some travel by

train.

109. Which of the following diagrams indicates the best relation between Profit, Dividend and

Bonus ?

A.

B.

C.

D.


Answer: Option B

Explanation:

Bonus and Dividend are different from each other. But both these are parts of profit

110. Which of the following diagrams indicates the best relation between Women, Mothers and

Engineers ?

A.

B.

C.

D.


Answer: Option A

Explanation:

All mothers are women and some mothers and some women may be engineers.

111. Which of the following diagrams indicates the best relation between Factory, Product and

Machinery ?

A.

B.

C.

D.


Answer: Option D

Explanation:

Product and Machinery are different from each other but both are found in Factory.

112. Which of the following diagrams indicates the best relation between Author, Lawyer and

Singer ?

A.

B.

C.

D.


Answer: Option B

Explanation:

All the three are different professions.

113. Which of the following diagrams indicates the best relation between Judge, Thieves and

Criminals ?

A.

B.

C.

D.


Answer: Option B

Explanation:

All the thieves are criminals while judge is different from these.

114. Which of the following diagrams indicates the best relation between Judge, Thieves and

Criminals ?

A.

B.

C.

D.

116. Which of the following diagrams indicates the best relation between Pigeon, Bird and Dog ?

A.

B.

C.

D.


Answer: Option A

Explanation:

All the pigeons are birds while dog is different from these.

117. Which of the following diagrams indicates the best relation between Earth, Sea and Sun ?

A.

B.

C.

D.


Answer: Option A

Explanation:

Sea is a part of Earth while Sun is different from these two.

118. Which of the following diagrams indicates the best relation between Hockey, Football and

Cricket ?

A.

B.

C.

D.


Answer: Option B

Explanation:

All these three games are different from each other.

119. One morning Udai and Vishal were talking to each other face to face at a crossing. If Vishal's

shadow was exactly to the left of Udai, which direction was Udai facing?

A. East B. West

C. North D. South


Answer: Option C

Explanation:

120. Y is in the East of X which is in the North of Z. If P is in the South of Z, then in which direction

of Y, is P?

A. North B. South

C. South-East D. None of these


Answer: Option D

Explanation:

P is in South-West of Y.

121. If South-East becomes North, North-East becomes West and so on. What will West become?

A. North-East B. North-West

C. South-East D. South-West


Answer: Option C

Explanation:

It is clear from the diagrams that new name of West will become South-East.

121. A man walks 5 km toward south and then turns to the right. After walking 3 km he turns to

the left and walks 5 km. Now in which direction is he from the starting place?

A. West B. South

C. North-East D. South-West

Answer: Option D

Explanation:

Hence required direction is South-West.

123. Rahul put his timepiece on the table in such a way that at 6 P.M. hour hand points to North. In

which direction the minute hand will point at 9.15 P.M. ?

A. South-East B. South

C. North D. West


Answer: Option D

Explanation:

At 9.15 P.M., the minute hand will point towards west.

124. Dev, Kumar, Nilesh, Ankur and Pintu are standing facing to the North in a playground such as

given below:

1. Kumar is at 40 m to the right of Ankur.

2. Dev is are 60 m in the south of Kumar.

3. Nilesh is at a distance of 25 m in the west of Ankur.

4. Pintu is at a distance of 90 m in the North of Dev.

1. Which one is in the North-East of the person who is to the left of Kumar?

A. Dev B. Nilesh

C. Ankur D. Pintu


Answer: Option D

Explanation:

Ankur is in the left of Kumar. Hence Pintu is in North-East of Ankur.

124. Each of the following questions is based on the following information:

1. Six flats on a floor in two rows facing North and South are allotted to P, Q, R, S, T and U.

2. Q gets a North facing flat and is not next to S.

3. S and U get diagonally opposite flats.

4. R next to U, gets a south facing flat and T gets North facing flat.

1. If the flats of P and T are interchanged then whose flat will be next to that of U?

A. P B. Q

C. R D. T


Answer: Option C

Explanation:

Hence flat R will be next to U.

126. Rasik walked 20 m towards north. Then he turned right and walks 30 m. Then he turns right

and walks 35 m. Then he turns left and walks 15 m. Finally he turns left and walks 15 m. In which

direction and how many metres is he from the starting position?

A. 15 m West B. 30 m East

C. 30 m West D. 45 m East


Answer: Option D

Explanation:

127. Solution:

Hank: pear apple cherry rose

Sam: cherry onion rose tulip

Paul: carrot gourd onion rose

Zick: aster rose tulip lily

Luke: pear nut gourd parsley

128. Solution:

The Spanish ship goes to Port Said and the French ship carries tea. However, tea can be carried by

the Brazilian ship, too.

If you understood position 'to the right' to mean anywhere on the right side from the given point

(not only right next to).

French 5:00 tea blue Genoa

Greek 6:00 coffee red Hamburg

Brazilian 8:00 cocoa black Manila

English 9:00 rice white Marseille

Spanish 7:00 corn green Port Said

129. Solution:

1 2 3 4 5

Name Bob Rachael Eilish Keeley Amy

Favorite TV

programme The Simpsons

Coronation

Street

Desperate

HousewivesNeighbours Eastenders

Destination France Italy Africa England Australia

Age 46 21 81 52 14

Where they live Town Youth Hostel Farm Village City

Hairstyle Bald Long Afro Curly Straight

130. Solution:

Holly did!

See below for full solution:

Person Alex Jackie Julieanne Cameron Holly

Flavor Vanilla Strawberry Banana Caramel Chocolate

Cookie Jar Mini Brass Tall Square Round

Brand Coles Dick Smith Paradise No Frills Arnotts

Cookie Choc chip Tiny Teddies 100s and 1000s Oreos Ginger

Place Lounge Bedroom Kitchen Closet Table

131. Solution:

Betty, Carol and Dan work in Administration department.

Earl works in the Marketing department.

132.

house 1 2 3 4 5

color yellow blue red green white

nationality norweigian dane brit german swede

drink water tea milk coffee beer

smoke dunhill blend pall mall prince bluemaster

pet cats horse birds fish dogs

134. Solution

888 + 88 + 8 + 8 + 8

(8(8(8+8)-(8+8)/8))-8

8888/8.888

(888-8) + 8×(8+8) – 8

((8×(8+8))-((8+8+8)/8))*8

(8+((8+8)/8))^((8+8+8)/8)

(8+((8+8)/8))^((88/8)-8)

((8×(8+8))-((88/8)-8))×8

(8888-888)/8

8(8×8+8×8)-8-8-8

135. Solution:

Tom's Granny is 58 years old. Let's see why:

First child born: Granny is 19

Second child born: Granny is 23 (19 + 4)

Third child born: Granny is 27 (23 + 4)

Fourth child born: Granny is 31 (27 + 4)

Fifth child born: Granny is 35 (31 + 4)

Sixth child born: Granny is 39 (35 + 4)

Sixth child is 19: Granny is 58 (39 + 19)

136. Solution:

The left number multiplied by 5 gives the total of the other two:

27 × 5 = 56 + 79

23 × 5 = 88 + 27

16 × 5 = 56 + ??

So ?? = 16 × 5 - 56 = 80 - 56 = 24

137. Solution:

The product of the two largest

minus the square of the smallest,

So the missing number is 45-16 = 29

138.

139. Solution:

Divide the 9 balls into 3 groups of 3. Compare the weight of two of those groups.

The heavier group should then be obvious, it will either tip the scales, or, if the scales stay balanced,

then it is the group you didn't include.

Now, choose 2 balls from this group and compare their weights, and using the same logic as before,

the heavier ball will be obvious.

140. Solution:

One possible method follows:

1. Fill up the 5 litre bucket

2. Pour the 5 litre bucket into the 3 litre bucket until the 3 litre bucket is full.

3. Empty the 3 litre bucket.

4. Pour the remaining 2 litres from the 5 litre bucket into the 3 litre bucket.

5. Fill up the 5 litre bucket again.

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Mental maths ix q & a