Question 1

A mother is 5 times older than her daughter. After 5 years, she would be 3 times older than her daughter. Find the mother's present age.

Accepted Answer

Question 2

The sum of ages of 4 children born at intervals of 4 years each is 60. What is the age of the youngest child?

Accepted Answer

Question 3

Nikhil is 8 years younger than his brother Rohan. How old will Rohan be when he is twice as old as Nikhil?

Accepted Answer

Suppose, the age of Nikhil is 1 year. Nikhil is 8 years younger than his brother Rohan. Therefore, age of Rohan = 1 + 8 = 9 years After 7 years , Nikhil will be 8 years old and Rohan will be 16 years old.

Question 4

The sum of present age of father and his son is 60 years. 6 years ago, father's age was 5 times the age of the son. After 6 years, son's age will be :

Accepted Answer

Question 5

The ages of Samir and Saurabh are in the ratio of 8 : 15 respectively . After 9 years the ratio of their ages will be 11 : 18. What is the difference between their ages in years?

Accepted Answer

Let the present ages of Samir and Saurabh are 8a and 15a years respectively ; . After 9 years the ages of Samir and Saurabh will be 8a + 9 and 15a + 9. According to question, After 9 years the ratio of their ages will be 11 : 18, then (8a + 9)/ = 11/18 ⇒ (8x + 9) x 18 = 11 x (15a + 9) ⇒ 144a + 162 = 165a + 99 ⇒ 21a = 63 ∴ a = 3 Hence, difference of their ages = 15a - 8a = 7a = 7 x 3 = 21 years

Question 6

The ratio of the present ages of Suresh and his daughter is 2 : 1. Six years hence, the ratio of their ages would be 23 : 13. Find the present age of Suresh?

Accepted Answer

Let the present ages of Suresh and his daughter be 2x and x years respectively; then According to question, Six years hence, the ratio of their ages would be 23 : 13 (2x + 6) / (x + 6) = 23/13 ⇒ (2x + 6) 13 = 23 (x + 6) ⇒ 26x + 78 = 23x + 138 ⇒ 3x = 60 ∴ x = 20 Hence, present age of Suresh = 2 x 10 = 40 years

Question 7

The present age of father is 34 years more than that of his son. 12 years ago, father's age was 18 times the age of his son. The present age of son in years is :

Accepted Answer

Let us assume the present ages of son be Y then his father present age will be Y + 34 years. then 12 years ago, father's age = Y + 34 -12 12 years ago, Son's age = Y - 12 Now according to question, 12 years ago, father's age was 18 times the age of his son. then 18( Y - 12 ) = Y + 34 - 12 ⇒ 18Y - 216 = Y + 22 ⇒ 17Y = 238 ∴ Y = 14 Hence, present age of his son = 14 years.

Question 8

The ratio of the ages of two persons is 4 : 7 and age of then is more than other by 30 years. The sum of their ages in years is:

Accepted Answer

Let the present ages of two person be 4x and 7x years respectively; then according to question, 7x = 30 + 4x ⇒ 3x = 30 ∴ x = 10 Hence, sum of their ages = 4x + 7x = 11x = 11 x 10 = 110 years

Question 9

A father is older than his first son by 30 years, the first son is older than the second son by 10 years. If the sum of their ages be 95 years, find the age of father.

Accepted Answer

Let us assume the age of second son be Y, then age of first son will be Y + 10 and age of father will be (Y + 10 + 30) years respectively; then according to question, sum of their ages be 95 years. x + x + 10 + x + 10 + 30 = 95 ⇒ 3x = 95 - 50 ⇒ 3x = 45 ∴ x = 15 age of the father = x + 10 + 30 Hence, age of the father = 15 + 10 + 30 = 55 years.

Question 10

The present age of Deepak is 3 time the present age of his son. Five years hence, the ratio of their ages will be 34 :13 respectively. The present age of Deepak is :

Accepted Answer

Let us assume the present age of son be x then present of Deepak be 3x. Five years hence, the ratio of their ages will be 34 : 13 respectively. then according to question, (3x + 5)/(x + 5) = 34/13 ⇒ (3x + 5) 13 = 34 (x + 5) ⇒ 39x + 65 = 34x + 170 ⇒ 5x = 105 ∴ x = 21 Hence, present age of Deepak = 3x = 3 x 21 = 63

Question 11

A mother is 25 years older than her daughter. Five years ago, the age of the mother was 6 times the age of the daughter. What is the present age of mother?

Accepted Answer

Let the present ages of mother and her daughter are ( x + 25 ) and x years respectively ; then Five years ago, the age of the mother was 6 times the age of the daughter. 6( x - 5 ) = x + 25 - 5 ⇒ 6x - 30 = x + 20 ⇒ 5x = 50 ∴ x = 10 Hence, the age of the mother = 10 + 25 = 35 years

Question 12

The difference between the present ages of P and Q is 4 years. The ratio of their ages after 5 years will be 9 : 8. The present age of P is :

Accepted Answer

Let us assume the present ages of P and Q be (x + 4) and x years; then, According to question, ( x + 4 + 5 )/ (x + 5) = 9/8 ⇒ 8x + 72 = 9x + 45 ∴ x = 27 Hence, present age of P = 27 + 4 = 31 years

Question 13

The present age of a father is three times the age of his son. Five years ago, father's age was four times the age of the son. What is the present age of son?

Accepted Answer

Let us assume that present age of son is P years then his father's present age will be 3P. According to question, Five years ago, father's age was four times the age of the son. Then 4 (P - 5) = 3P - 5 ⇒ 4P - 20 = 3P - 5 ∴ P = 15 years The present age of Son is 15 Years.

Question 14

The respective ratio of the ages of Shami, Nammi and Pammi is 3 : 4 : 5. The sum of their ages is 48 years. What will be the respective ratio of their ages 8 years hence?

Accepted Answer

Let the present ages of Shami, Nammi and pammi are 3x, 4x and 5x years respectively; then, According to question, 3x + 4x + 5x = 48 ⇒ 12x = 48 ∴ x= 4 Hence, their present ages are 12, 16 and 20 years respectively. So, required ratio = (12 + 8) : (16 + 8) : (20 + 8) = 20 : 24 : 28 = 5 : 6 : 7

Question 15

5 years ago, the average age of Ram and Shyam was 20 years. Now, the average age of Ram, Shyam and Mohan is 30 years. What will be Mohan's age 10 years hence?

Accepted Answer

Let us assume the present age of Ram R, Shyam S and Mohan M. 5 years ago, Ram age = R - 5 5 years ago, Shyam age = S - 5 5 years ago, Mohan age = M - 5 According to question, 5 years ago, the average age of Ram and Shyam was 20 years, (5 years ago, Ram age + 5 years ago, Shyam age) /2 = 20 (R - 5 + S - 5 )/2 = 20 R + S = 40 + 10 = 50 ................(1) Now Again according to question, Now , the average age of Ram, Shyam and Mohan is 30 years (R + S + M)/3 = 30 R + S + M = 90 Pu the value of R + S from equation (1) 50 + M = 90 M = 90 - 50 = 40 The present age of Mohan = 40 years 10 years hence, the age of Mohan = 40 + 10 = 50 years

Question 16

The difference between the ages of a boss and his subordinate is 16 years. Four years ago, the respective ratio of the ages of the boss and subordinate was 11 : 7. The present age of the subordinate is:

Accepted Answer

Let us assume the present age of the subordinate is P then her subordinate age will be (P + 16). According to Question, Four years ago, the respective ratio of the ages of the boss and subordinate was 11 : 7. (P +16 - 4 )/ (P - 4) = 11/7 ⇒ 7 x (P +16 - 4 ) = 11 x (P - 4) ⇒ 7 x (P +12 ) = 11 x (P - 4) ⇒ 7P + 84 = 11P - 44 ⇒ 4P = 128 ∴ P = 32 years

Question 17

The average age of a cricket team is 27 years. Two players with 24 and 27 years of age are replaced by new players of 23 and 28 years of age. What is the average age of the team now?

Accepted Answer

According to question , The average age of a cricket team = 27 years Age of two old players = 24 + 27 = 51 Age of two new players = 23 + 28 = 51 ∴ New average age of a cricket team = 27 + ( Age of two old players ) - ( Age of two new players ) New average age of a cricket team = 27 + ( 51 ) - ( 51 ) = 27 years In other words ,The total age of the two players which were replaced is the same as that of the total age of two players which replaced them. Therefore, the new average will remain unchanged.

Question 18

The age of X is 2/3 rd that of Y. After 6 years X will be 46 years old. What is the present age of Y?

Accepted Answer

Question 19

A, B, C, D, are four friends. Average age of A and C is 35 years and that of B, and D is 40 years. Average age of B, C and D is 40 years. The sum of the ages of A and D is equal to that of B and C. Find out the ages (in years) of A, B, C and D.

Accepted Answer

Given :- Average age of A and C = 35 years ⇒ A + C = 70 years ......... ( ⅰ ) Average age of B, and D = 40 years. ⇒ B + D = 80 years ......... ( ⅱ ) and Average age of B, C and D = 40 years. ⇒ B + C + D = 120 years ......... ( ⅲ ) With the help of equations ( ⅰ ) , ( ⅱ ) and ( ⅲ ) , we get ∴ age of C = 40 years and age of A = 30 years According to question , ∴ age of A + age of D = age of B + age of C ⇒ A + D = B + C ⇒ 30 + D = B + 40 ⇒ D – B = 10 ∴ age of B = 35 years and age of D = 45 years

Question 20

The difference between a mother's age and the sum of her two daughters' age is 6. The average age of two daughters is 22. What is the age of mother?

Accepted Answer

According to question , Mother's age - Sum of her two daughters' age = 6. The average age of two daughters = 22 Total age of two daughters = 22 × 2 = 44 years ∴ The age of their mother = Total age of two daughters + 6 years The age of their mother = 44 + 6 = 50 years

Problems on Ages Questions