The ages of Rima and Bina are in the ratio 9 : 8 respectively. After 5 years, the ratio of their ages will be 10 : 9. What is the difference in their ages?

Question: The ages of Rima and Bina are in the ratio 9 : 8 respectively. After 5 years, the ratio of their ages will be 10 : 9. What is the difference in their ages?

Solution:
Let Rima’s age be = 9x years.
Then Bina’s age = 8x years

According to the question,
(9x + 5)/(8x + 5) = 10/9
⇒ 9(9x + 5) = 10(8x + 5)
⇒ 81x + 45 = 80x + 40
⇒ 81x - 80x = 40 - 45
⇒ - x = - 5
∴ x = 5

∴ The difference in their ages = 9x - 8x = x = 5 years.