Question 1

A is three times as old as B. C was twice-as old as A four years ago. In four years' time, A will be 31. What are the present ages of B and C?

Accepted Answer

We have : A = 3B ...(i) and C - 4 = 2 (A - 4) ...(ii) Also, A + 4 = 31 or A= 31-4 = 27. Putting A = 27 in (i), we get: B = 9. Putting A = 27 in (ii), we get C = 50.

Question 2

Ravi's brother is 3 years senior to him. His father was 28 years of age when his sister was born while his mother was 26 years of age when he was born. If his sister was 4 years of age when his brother was born, what were the ages of Ravi's father a…

Accepted Answer

When Ravi's brother was born, let Ravi's father's age = x years and mother's age = y years. Then, sister's age = (x - 28) years. So, x - 28 = 4 or x = 32. Ravi's age = (y - 26) years. Age of Ravi's brother = (y - 26 + 3) years = (y - 23) years. Now, when Ravi's brother was born, his age = 0 i.e. y - 23 = 0 or y = 23.

Question 3

A number of friends decided to go on a picnic and planned to spend Rs. 96 on eatables. Four of them, however, did not turn up. As a consequence, the remaining ones had to contribute Rs. 4 each extra. The number of those who attended the picnic was

Accepted Answer

Question 4

A father is now three times as old as his son. Five years back, he was four times as old as his son. The age of the son (in years) is

Accepted Answer

Let son's age be x years. Then, father's age = (3x) years. Five years ago, father's age = (3x - 5) years and son's age = (x - 5) years. So, 3x - 5 = 4 (x - 5) ⟺ 3x - 5 = 4x - 20 ⟺ x = 15.

Question 5

A pineapple costs Rs. 7 each. A watermelon costs Rs. 5 each. X spends Rs. 38 on these fruits. The number of pineapples purchased is

Accepted Answer

Question 6

A bus starts from city X. The number of women in the bus is half of the number of men. In city Y, 10 men leave the bus and five women enter. Now, number of men and women is equal. In the beginning, how many passengers entered the bus?

Accepted Answer

Originally, let number of women = x. Then, number of men = 2x. So, in city Y, we have : (2x - 10) = (x + 5) or x - 15. Therefore Total number of passengers in the beginning = (x + 2x) = 3x = 45.

Question 7

In a class of 60 students, the number of boys and girls participating in the annual sports is in the ratio 3 : 2 respectively. The number of girls not participating in the sports is 5 more than the number of boys not participating in the sports. If …

Accepted Answer

Let the number of boys and girls participating in sports be 3x and 2x respectively. Then, 3x = 15 or x = 5. So, number of girls participating in sports = 2x = 10. Number of students not participating in sports = 60 - (15 + 10) = 35. Let number of boys not participating in sports be y. Then, number of girls not participating in sports = (35 -y). Therefore (35 - y) = y + 5 ⟺ 2y ⟺ 30 ⟺ y = 15. So, number of girls not participating in sports = (35 - 15) = 20. Hence, total number of girls in the class = (10 + 20) = 30.

Question 8

In a family, the father took 1/4 of the cake and he had 3 times as much as each of the other members had. The total number of family members is

Accepted Answer

Question 9

A shepherd had 17 sheep. All but nine died. How many was he left with?

Accepted Answer

'All but nine died' means 'All except nine died' i.e. 9 sheep remained alive.

Question 10

12 year old Manick is three times as old as his brother Rahul. How old will Manick be when he is twice as old as Rahul?

Accepted Answer

Manick's present age = 12 years, Rahul's present age = 4 years. Let Manick be twice as old as Rahul after x years from now. Then, 12 + x = 2 (4 + x) ⟺ 12 + x = 8 + 2x ⟺ x = 4. Hence, Manick's required age = 12 + x = 16 years.

Question 11

In a city, 40% of the adults are illiterate while 85% of the children are literate. If the ratio of the adults to that of the children is 2 : 3, then what percent of the population is literate?

Accepted Answer

Question 12

A waiter's salary consists of his salary and tips. During one week his tips were 5/4 of his salary. What fraction of his income came from tips?

Accepted Answer

Question 13

Two bus tickets from city A to B and three tickets from city A to C cost Rs. 77 but three tickets from city A to B and two tickets from city A to C cost Rs. 73. What are the fares for cities B and C from A?

Accepted Answer

Let Rs. x be the fare of city B from city A and Rs. y be the fare of city C from city A. Then, 2x + 3y = 77 ...(i) and 3x + 2y = 73 ...(ii) Multiplying (i) by 3 and (ii) by 2 and subtracting, we get: 5y = 85 or y = 17. Putting y = 17 in (i), we get: x = 13.

Question 14

If 100 cats kill 100 mice in 100 days, then 4 cats would kill 4 mice in how many days?

Accepted Answer

Question 15

A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has?

Accepted Answer

Let number of notes of each denomination be x. Then, x + 5x + 10x = 480 ⟺ 16x = 480 ⟺ x = 30. Hence, total number of notes = 3x = 90.

Question 16

Mac has £ 3 more than Ken, but then Ken wins on the horses and trebles his money, so that he now has £ 2 more than the original amount of money that the two boys had between them. How much money did Mac and Ken have between them before Ken's win?

Accepted Answer

Let money with Ken = x. Then, money with Mac = x + £ 3. Now, 3x = (x + x + £ 3) + £ 2 ⟺ x = £ 5. Therefore Total money with Mac and Ken = 2x + £ 3 = £ 13.

Question 17

Ayush was born two years after his father's marriage. His mother is five years younger than his father but 20 years older than Ayush who is 10 years old. At what age did the father get married?

Accepted Answer

Ayush's present age = 10 years. His mother's present age = (10 + 20) years = 30 years. Ayush's father's present age = (30 + 5) years = 35 years. Ayush's father's age at the time of Ayush's birth = (35 - 10) years = 25 years. Therefore Ayush's father's age at the time of marriage = (25 - 2) years = 23 years.

Question 18

If you write down all the numbers from 1 to 100, then how many times do you write 3?

Accepted Answer

Clearly, from 1 to 100, there are ten numbers with 3 as the unit's digit- 3, 13, 23, 33, 43, 53, 63, 73, 83, 93; and ten numbers with 3 as the ten's digit - 30, 31, 32, 33, 34, 35, 36, 37, 38, 39. So, required number = 10 + 10 = 20.

Question 19

In three coloured boxes - Red, Green and Blue, 108 balls are placed. There are twice as many balls in the green and red boxes combined as there are in the blue box and twice as many in the blue box as there are in the red box. How many balls are the…

Accepted Answer

Let R, G and B represent the number of balls in red, green and blue boxes respectively. Then, . R + G + B = 108 ...(i), G + R = 2B ...(ii) B = 2R ...(iii) From (ii) and (iii), we have G + R = 2x 2R = 4R or G = 3R. Putting G = 3R and B = 2R in (i), we get: R + 3R + 2R = 108 ⟺ 6R = 108 ⟺ R = 18. Therefore Number of balls in green box = G = 3R = (3 x 18) = 54.

Question 20

A motorist knows four different routes from Bristol to Birmingham. From Birmingham to Sheffield he knows three different routes and from Sheffield to Carlisle he knows two different routes. How many routes does he know from Bristol to Carlisle?

Accepted Answer

Total number of routes from Bristol to Carlisle = (4 x 3 x 2) = 24.

Arithmetic Reasoning Questions