One year ago, the ratio of Rahul's and Amir's age was 6 : 7 respectively. Four years hence, this ratio would become 7 : 8. How old is Amir?

Question: One year ago, the ratio of Rahul's and Amir's age was 6 : 7 respectively. Four years hence, this ratio would become 7 : 8. How old is Amir?

Solution:
Let Rahul's and Amir's ages one year ago be 6x and 7x years respectively.
Then,
Rahul's age 4 years hence = (6x + 1) + 4 = (6x + 5) years.
And Amir's age 4 years hence = (7x + 1) + 4 = (7x + 5) years.

Therefore,
(6x + 5) : (7x + 5) = 7 : 8
⇒ (6x + 5)/(7x + 5) = 7/8
⇒ 8(6x + 5) = 7(7x + 5)
⇒ 48x + 40 = 49x + 35
∴ x = 5

Hence, Amir's present age = (7x + 1) = 35 + 1 = 36 years