Multiple choice

The respective ratio between the present ages of A and B is (3 : 4) and that of B and C is (6 : 5). 9 years ago, the sum of the ages of A and C was 58 years. Find present age of B.

  1. 36 years

  2. 48 years

  3. 45 years

  4. 30 years

  5. None of these
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B Correct answer
Explanation

A:B = 3:4 and B:C = 6:5. Making B equal: A:B = 9:12 and B:C = 12:10, so A:B:C = 9:12:10. 9 years ago, A + C = 58, so 9x + 10x = 58, giving x = 2.81. Current ages: A = 9(2.81) + 9 ≈ 34.3, B = 12(2.81) + 9 ≈ 42.7. However, solving differently: Let current ages be 9k, 12k, 10k. Then 9k + 10k - 18 = 58, so 19k = 76, k = 4. B = 12(4) = 48 years. The answer is correct.

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