Question

If twice the son’s age in years is added to the mother’s age, the sum is 70 years. But, if twice the mother’s age is added to the son’s age, the sum is 95 years. Find the age of the mother and that of the son.

Answer 1

Let the mother’s present age be x years.
Let her son’s present age be y years.
Then, we have:
x + 2y = 70                              …….(i)
And, 2x + y = 95                      ……(ii)

On multiplying (ii) by 2, we get:
4x + 2y = 190                            ……..(iii)
On subtracting (i) from (iii), we get:
3x = 120
⇒ x = 40
On substituting x = 40 in (i), we get:
40 + 2y = 70
⇒ 2y = (70 – 40) = 30
⇒ y = 15
Hence, the mother’s present age is 40 years and her son’s present age is 15 years.