### AGE PROBLEMS QUIZ 001

- Ten years ago, Kumar was thrice as old as Sailesh was but 10 years hence, he will be only twice as old. Find Kumar’s present age.

(a) 60 years

(b) 80 years

**(c) 70 years**

(d) 76 years

(e) None of these

Explanation:

Let Kumar’s present age be x years and Sailesh’s present age be y years.

Then, according to the first condition,

x – 10 = 3(y – 10) or, x – 3y = – 20 ..(1)

Now. Kumar’s age after 10 years = (x + 10) years

Sailesh’s age after 10 years = (y + 10)

(x + 10) = 2 (y + 10) or, x – 2y = 10 ..(2)

Solving (1) and (2), we get x = 70 and y = 30

Kumar’s age = 70 years and Sailesh’s age = 30 years..

- Five years hence, father’s age will be three times the age of his son. Five years ago, father was seven times as old as his son. Find their present ages.

**(a) 40 years and 10 years**

(b) 42 years and 12 years

(c) 35 years and 5 years

(d) 41 years and 11 years

(e) None of these

Explanation:

Let the present age of father be x years and the present age of son be y years.

five year’s hence

x + 5 = 3(y + 5)

=>x – 3y -10 = 0 —–(1)

Five year’s ago

x – 5 = 7(y – 5)

=>x – 7y + 30 = 0 —–(2)

Solving Equations (1) and (2), we get

x = 40 and y = 10

Hence, present age of father is 40 years and present age of son is 10 years.

- A person’s present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present?

(a) 32

(b) 36

(c) 38

**(d) 40**

(e) None of these

Explanation:

Let the mother’s age be x

Present age of the person = 2/5x

(2/5)x+8 = 0.5x +4

on solving we get x = 40

- The age of father 10 years ago was thrice the age of his son. Ten years hence, father’s age will be twice that of his son. The ratio of their present ages is:

(a) 5:2

**(b) 7:3**

(c) 9:2

(d) 13:4

(e) None of these

Explanation:

Let the ages of father and son 10 years ago be 3x and x years respectively.

Then, (3x + 10) + 10 = 2[(x + 10) + 10]

3x + 20 = 2x + 40

x = 20.

Required ratio = (3x + 10) : (x + 10) = 70 : 30 = 7 : 3.

- Sachin is younger than Rahul by 7 years. If their ages are in the respective ratio of 7 : 9, how old is Sachin?

(a) 16

(b) 18

(c) 28

**(d) 24.5**

(e) None of these

Explanation:

Let Rahul’s age be x years.

Then, Sachin’s age = (x – 7) years.

x – 7 /x = 7/ 9

9x – 63 = 7x

2x = 63

x = 31.5

Hence, Sachin’s age =(x – 7) = 24.5 years.

- The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).

(a) 8, 20, 28

**(b) 16, 28, 36**

(c) 20, 35, 45

(d) 21, 30, 42

(e) None of these

Explanation:

Let their present ages be 4x, 7x and 9x years respectively.

Then, (4x – 8) + (7x – 8) + (9x – 8) = 56

20x = 80

x = 4.

Their present ages are 4x = 16 years, 7x = 28 years and 9x = 36 years respectively.

- Suresh has three daughters namely Ramya, Anita and Kiran. Ramya is the eldest daughter of Mr. Suresh while Kiran is the youngest one. The present ages of all three of them are square numbers. The sum of their ages after 5 years is 44. What is the age of Ramya after two years?

(a) 15 years

(b) 13 years

**(c) 18 years**

(d) 17 years

(e) 16 years

Explanation:

Square numbers – a, b, c

(a + 5) + (b + 5)+ (c + 5) = 44

a + b + c = 44 – 15 = 29

Possible values of a, b, c = 4, 9, 16 [Out of 1, 4, 9, 16, 25]

Ramya’s present age = 16; after two years = 18

- Ajay got married 6 years ago. His present age is 5/4 times his age at the time of his marriage. Ajay’s brother was 5 years younger to him at the time of his marriage. What is the present age of Ajay’s brother?

(a) 22 years

(b) 11 years

**(c) 25 years**

(d) 19 years

(e) 15 years

Explanation:

Present age of Ajay = x ; Present age of Ajay’s sister = y

x = (x-6)(5/4)

x = 30

present age of Ajay’s brother = 30 – 5 = 25

- The ratio between the present ages of A and B is 6:7. If B is 4 years older than A. What will be the ratio of the ages of A and B after 4 years?

(a) 8:7

**(b) 7:8**

(c) 1:8

(d) Data inadequate

(e) None of these

Explanation:

Let A’s age and B’s age be 6X years and 7X years respectively

Then, 7X – 6X = 4

X = 4

Required ratio = (6X + 4) : (7X + 4) = (6*4+4) : (7*4 +4) =28 : 32 = 7 : 8

- Ram’s present age is three times his son’s present age and two-fifth of his father’s present age. The average of the present ages of all of them is 46 years. What is the difference between the Ram’s son’s present age and Ram’s father’s present age?

(a) 68 years

(b) 88 years

(c) 58 years

(d) can not determined

(e) None of these

Explanation:

- The ratio of the ages of Anil and his son at present is 7 : 3. Six year hence, the ratio of the ages of the Anil’s wife and the son will be 2 : 1. Find the ratio of the present ages of Anil and his wife.

(a) 6 : 5

(b) 4 : 3

(c) 5 : 4

**(d) Cannot be determined.**

(e) None of these

Explanation:

Let the present age of Anil and his son be 7x years and 3x years respectively.

Let the present age of the son’s mother be m years.

(m + 6) / (3x + 6) = 2 / 1

m + 6 = 6x + 12

m = 6x + 6

The ratio of the present ages of Anil and his wife =

7x / (6x + 6)

This cannot be found uniquely.

- Five years ago, Mr Sunil was thrice as old as his son and ten years hence he will be twice as old as his son. Mr. Sunil’s present age (in years) is

(a) 35

(b) 45

**(c) 50**

(d) 55

(e) None of these

Explanation:

Let Mr. Sunil’s age (in years) = X and his son’s age = Y

Then, X – 5 = 3(Y – 5)

i.e., X – 3Y + 10 = 0 —– ’(1)

and, X + 10 = 2(Y + 10)

i.e. X – 2Y – 10 = 0 —– (2)

Solving (1) and (2), we get Y = 20

Substituting Y in eq (1), we get X = 50

Hence, the present age of the father is 50.

- If the present age of A be is twice the present age of B. 18 years ago age of C was half the age of B six years hence. If the average of the present ages of A, B and C is 42 years. Find the age of A, 9 years hence?

**(a) 69 years**

(b) 70 years

(c) 73 years

(d) 77 years

(e) None of these

Explanation:

- Ten years ago, the ages of the members of a joint family of eight people added up to 231 years. Three years later, one member died at the age of 60 years and a child was born during the same year. After another three years, one more member died, again at 60, and a child was born during the same year. The current average age of this eight-member joint family is nearest to

(a) 21 years

(b) 25 years

**(c) 24 years**

(d) 23 years

(e) None of these

Explanation:

- A boy was asked of his age by his friend. The boy said, “The number you get when you subtract 25 times my age from twice the square of my age will be thrice your age.” If the friend’s age is 14, then the age of the boy is

(a) 28 years

(b) 21 years

**(c) 14 years**

(d) 25 years

(e) None of these

Explanation:

- Published in AGE PROBLEMS