One year ago, the ratio of Amit’s and Arun’s ages was 6 : 7 respectively. Four years hence, their ages will be in the ratio 7 : 8. How old is Amit?

Given,

The ratio of Amit’s and Arun’s ages was 6 : 7.

Let Amit's age one year ago be 6x and Arun's age one year ago be 7x.

Their present ages are :

Amit's present age = 6x + 1

Arun's present age = 7x + 1

After four years their ages will be:

Amit's age will be (6x + 1) + 4 = 6x + 5

Arun's age will be (7x + 1) + 4 = 7x + 5

Given,

The ratio of their ages four years hence will be 7 : 8.

$\therefore \dfrac{6x + 5}{7x + 5} = \dfrac{7}{8}$

⇒ 8(6x + 5) = 7(7x + 5)

⇒ 48x + 40 = 49x + 35

⇒ 40 - 35 = 49x - 48x

⇒ x = 5

Amit's present age is 6x + 1.

= 6(5) + 1 = 30 + 1

= 31 years.

Hence, Amit's present age = 31 years.