Seven years ago, the ratio of the ages of A and B was 4 : 5. Eight years hence, the ratio of the ages of A and B will be 9 : 10. What is the difference between their present ages in years?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e 3.
Seven years ago, the ratio of the ages of A and B was 4 : 5 = 4x : 5x
Present age = (4x + 7) : (5x + 7)
Eight years hence, the ratio of the ages of A and B will be 9 : 10
⇒ (4x + 7 + 8)/(5x + 7 + 8) = 9/10
⇒ 10(4x + 15) = 9(5x + 15)
⇒ 40x + 150 = 45x + 135
⇒ 5x = 15
⇒ x = 3
Present age of A = 4x + 7 = 12 + 7 = 19
Present age of B = 5x + 7 = 15 + 7 = 22
Required difference = 22 - 19 = 3 years