Multiple choice

A's age six years ago was equal to twice of B's age four years ago. C is nine years elder to B and also nine years younger than A. What is the sum of the present ages of A, B and C?

  1. 90 years

  2. 64 years

  3. 65 years

  4. 87 years

  5. 81 years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let ages be A, B, C. A-6 = 2(B-4) => A-6 = 2B-8 => A = 2B-2. C = B+9. C = A-9 => B+9 = A-9 => A = B+18. Equating: 2B-2 = B+18 => B = 20. Then A = 38, C = 29. Sum = 38+20+29 = 87.

AI explanation

Let the present ages of A, B and C be A, B and C; the conditions give A - 6 = 2(B - 4), C = B + 9 and A = C + 9. By substituting the equations for C and A, we get B + 9 + 9 - 6 = 2B - 8, which simplifies to B + 12 = 2B - 8, meaning B is 20. Then C is 29 and A is 38, making their total sum 20 + 29 + 38 = 87. The result is 87 years.

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