Question

A man is `3 1/2` times as old as his son. If the sum of the squares of their ages is 1325, find the ages of the father and the son.

Answer 1

Given: Let the son’s present age = x years.

Then the man’s (father’s) age = `3 1/2 x = (7/2)x`.

`(7/2 x)^2 + x^2 = 1325`

`(49/4)x^2 + x^2 = 1325`

`(49/4 + 4/4)x^2 = 1325`

⇒ `(53/4)x^2 = 1325`

`x^2 = 1325 xx (4/53)`

= 25 × 4

= 100

x = 10   ...(Age must be positive)

Father’s age = `(7/2) xx 10 = 35`

Son = 10 years, Father = 35 years.