Question

A man present age is two-fifth of the age of his mother after 8 years he will be 1 half of the age of his mother at that time how old is the mother at present

Answer 1

let the present age of man is x years and his mother's present age is y years.
$x = \frac{2}{5} y \\ 5x - 2y = 0 \\ x + 8 = \frac{1}{2} (y + 8) \\ 2x + 16 - y - 8 = 0 \\ 2x - y = - 8 \\ multiply \: eq2 \: by \: 2 \: and \: subtract \: both \: equation \\ 5x - 2y = 0 \\ 4x - 2y = - 16 \\ x = 16 \\ 2(16) - y = - 8 \\ - y = - 8 - 32 \\ - y = - 40 \\ y = 40$
man age is 16 years and mother' s age is 40 years

Answer 2

Answer:

Let the mother age be x years.

Then, the persons present age will be 2/5 x years.

According to Question now,

(2/5 x + 8) = 1/2 x + 8

2(2x + 40) = 5(x + 8)

x = 40 years.