The present ages of A and B are in the ratio 9 : 10. The ratio of their ages 8 years from now will be 11 : 12. What will be the sum of their ages (in years) 3 years from now?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 82.
Let the present ages of A and B be 9x and 10x respectively
8 years hence, the ages of A and B will be (9x + 8) and (10x + 8) respectively
As per the question;
⇒ (9x + 8)/(10x + 8) = 11/12
⇒ 12(9x + 8) = 11(10x + 8)
⇒ 108x + 96 = 110x + 88
⇒ 2x = 8
⇒ x = 4
The present age of A = 9x = 9 × 4 = 36 years, and the present age of B = 10x = 10 × 4 = 40 years
A's age after 3 years = 36 + 3 = 39 years and,
B's age after 3 years = 40 + 3 = 43 years
Thus,
The sum of their ages after 3 years = 39 + 43 = 82 years