Question

Forty years hence, Mr. Pratap’s age will be the square of what it was 32 years ago. Find his present age.

Answer 1

Let Partap’s present age = x years
40 years hence his age = x + 40
and 32 years ago his age = x – 32
According to the condition
x + 40 = (x - 32)²
⇒ x + 40 = x² – 64x + 1024
⇒ x² – 64x + 1024 – x – 40 = 0
⇒ x² – 65x + 1024 – x – 40 = 0
⇒ x² – 65x + 984 = 0
⇒ x² – 24x – 41x + 984 = 0
⇒ x(x – 24) – 41(x – 24) = 0
⇒ (x – 24)(x – 41) = 0
EIther x – 24 = 0,
then x = 24
but it is not possible as it is less than 32
or
x – 41 = 0,
then x = 41
Hence present age = 41 years.