Question

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

Answer 1

Hello friend !

Answer is given below:

Let the present age of the mother be x .

Then the present age of the person will be $\frac{2}{5} x$ ( As per the question)

After  8 years the age of the mother will be = x + 8

And the age of the person 8 years later will be =  $\frac{2}{5} x$ + 8

But as given in the question the age of the person  8 years later is equal to half of the age of the mother

This implies that 

 $\frac{2}{5} x$ + 8 = (x + 8)/2

⇒ (2x + 40)/5 = (x + 8)/2

⇒ 4x + 80 = 5x + 40

⇒ 80 - 40 =  5x - 4x 

⇒ 40 = x 

Therefore the present age of mother is = 40 years .

Hope this helps !!!

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.