Multiple choice

The average of the ages of A, B and C 3 years hence from now would be 35 years. A's present age is (\frac{7}{17}) of the sum of the present ages of B and C. If the ratio of present ages of B and C is 9: 8, respectively, then what is the difference between the present ages of A and C?

  1. 5

  2. 8

  3. 4

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

3 years hence average age = 35, so total age then = 105. Present total age = 105 - 9 = 96. Let present ages be A, B, C. A = (7/17)(B + C) = (7/17)(96 - A). Solving: 17A = 672 - 7A gives 24A = 672, A = 28. B:C = 9:8, B + C = 68. So B = 36, C = 32. Difference A - C = 28 - 32 = -4, |A - C| = 4.

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