Multiple choice

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?

  1. 4

  2. 2

  3. 3

  4. 6
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let A and B's ages 7 years ago be 4x and 5x. Their present ages are 4x+7 and 5x+7. Eight years hence, their ages will be 4x+15 and 5x+15. The ratio (4x+15)/(5x+15) = 9/10 leads to 40x + 150 = 45x + 135, so 5x = 15, x = 3. The difference in their ages is 5x - 4x = x = 3.

AI explanation

Let the present ages of A and B be 4x + 7 and 5x + 7 based on their ratio seven years ago. Eight years hence, their ages will be 4x + 15 and 5x + 15, so (4x + 15) / (5x + 15) = 9 / 10. Solving 40x + 150 = 45x + 135 gives x = 3, making their present ages 19 and 22. The difference between their present ages is 22 - 19 = 3 years.

Keep practicing — related questions