Problems Based on Age

Question 1: The age of Rekha is twelve times that of her daughter Avani. If the age of Avani is 3 years, what is the age of Rekha?

Solution. Who’s age do we need? Rekha’s.
                 Present age required to be found? Yes!

Okay, so, Rekha’s present age = x

Rekha’a age is 12 times her daughter’s age.

Daughter’s age = 3. Therefore, 12 times of 3 = x

12 x 3 = x
= 36 years = Rekha’s age.

Question 2: The father’s age four years ago was 8 times the age of his son. At present the father’s age is 4 times that of his son. Find the son’s present age.

Solution. Okay, who’s present age do we need to find? Son’s.
Therefore, Son’s present age = x

We’ll first make the present age’s equation with dad and son – only ‘cause it makes things easier to proceed from the present!

‘At present the father’s age is 4 times that of his son’, i.e., Father’s present age = 4x.

‘Father’s age four years ago was 8 times the age of his son’ – ‘four years ago’ will simple mean, subtracting 4 from the present ages of BOTH father and son; and the whole equation will stand as :

(4x – 4) = 8 x (x – 4)
Solving it – x = 7 years,

The son’s present age = 7 years. Easy does it, doesn’t it?


Question 3: At present, the ratio between the ages of Amar and Norman is 4:3. After 6 years, Amar’s age will be 26 years. What is the age of Normanat present?

Solution. Who’s ‘present’ age do we need to find? Norman’s.

But they have also have given the ration of present ages, 4:3.

So we can use ‘x’ to denote both their present ages to be 4x and 3x, i.e., Amar’s and Norman’s respectively.

Next, ‘Amar’s age 6 years later’, = (4x + 6) = 26.
x = 5 years.

Norman’s present age = 3x = 3 x 5 = 15 years.

Question 4: The ratio of the father’s age to the son’s age is 4:1 the product of their ages is 196. What will the ratio of their ages after 5 years?

Ans.: 11:4


Question 5: Sam’s age is one-fourth of his father’s age and two-third of his sister Rita’s. What is the ratio of the ages of Sam, Rita and their father respectively?

Ans.: 2:3:8


Question 6: The average age of boys in a class of 30 is 15 years. If 10 more boys join the class, the average of the whole class gets reduced by a year. What is the average age of newcomers? [This mixes age and average – a real IBPS worthy question!]

Ans.: 11years


Question 7: Present age of Vinny is 8 lesser than Amu’s present age. If 3 years ago Amu’s age was X, what will be Vinny’s present age?

Ans.: (X-5) years


Question 8: The ratio between the present ages of P and R is 5:3. The ratio between P’s age four years ago and R’s age four years hence is 1:1. What is the ratio between P’s age 4 years hence and B’s age four years ago? [‘Hence’ means future. And this is one gem of a question!]

Ans.: 3:1

Question 9: The ratio between the present ages of Doom and Room is 2:3. 4 years ago the ratio between their ages was 5:8. What will be Doom’s age after 7 years?

Ans.: 31 years


Question 10: The age of Rani is 5 times the age of her daughter. After 12 years the age of Rani will be thrice the age of her daughter. Find the present age of Rani’s daughter.

Ans.: 12 years.