Multiple choice

The ratio of ages of A and B, 8 years ago, was (2: 3). Four years ago, the ratio of their ages was (5: 7). What will be the ratio of their ages 8 years from now?

  1. 4: 5

  2. 3: 4

  3. 7: 8

  4. 5: 6
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A Correct answer
Explanation

Let ages 8 years ago be 2x and 3x, so current ages are 2x+8 and 3x+8. Four years ago, ages were 2x+4 and 3x+4, and the ratio was 5:7. So (2x+4)/(3x+4) = 5/7, giving 14x+28 = 15x+20, so x = 8. Current ages are 24 and 32. Eight years from now, ages will be 32 and 40, giving ratio 32:40 = 4:5. Option B (3:4) would result from incorrect age calculations, and Options C and D don't match the computed ratio.

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