A's present age is two-fifth of the age of his mother. After 8 years, his age will be half of the age of his mother. How old is the mother at present?

40 years

Let us consider that ,

present Age of A = A years  and present Age of mother is M years

A's present age is two-fifth of the age of his mother

A = 2/5 × M     ------(1)

After 8 years ,

Age of A = A + 8

Age of Mother = M + 8

According to question,

A + 8  = 1/2× ( M + 8)   ----(2)

By using equation (1)

2/5 × M + 8  = 1/2× ( M + 8)

2/5 × M + 8  = 1/2× M + 4

2/5 × M  - 1/2× M   = 4- 8

 ( 4 - 5 ) /10× M = - 4

M = 40

So, Age of Mother is 40 years.

The correct answer is Option (1) → 40 years