If 5 years ago, the ratio of age of Hasan and Rina was 1 : 2 and after 15 years from present their ratio would be 5 : 6. Find the age of Rina after 20 years.

Question: If 5 years ago, the ratio of age of Hasan and Rina was 1 : 2 and after 15 years from present their ratio would be 5 : 6. Find the age of Rina after 20 years.

Solution:
Let, present age of Hasan be x
and present age of Rina be y.

Then, according to question
(x - 5)/(y - 5) = 1/2
⇒ 2x - 10 = y - 5
⇒ x = (y + 5)/2 .............(1)

Also,
(x + 15)/(y + 15) = 5/6
⇒ 6x + 90 = 5y + 75
⇒ 6x + 15 = 5y

Putting value of x from equation 1, we get
3y + 15 + 15 = 5y
⇒ 2y = 30
⇒ y = 15

∴ Age of Rina after 20 years = 15 + 20 = 35 years.