Multiple choice

$A$ is three times as old as $B$. $C$ was twice-as old as $A$ four years ago. In four years' time, $A$ will be $31$. What are the present ages of $B$ and $C$?

  1. $9, 46$
  2. $9, 50$
  3. $10, 46$
  4. $10, 50$
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B Correct answer
Explanation

A = 3B. C - 4 = 2(A - 4). A + 4 = 31 => A = 27. Then B = 27/3 = 9. C - 4 = 2(27 - 4) = 2(23) = 46 => C = 50. Ages are 9 and 50.

AI explanation

Let the present ages of A, B, and C be A, B, and C. Since A + 4 = 31, A is currently 27. Because A is three times as old as B, B is 27 / 3 = 9. Four years ago, A was 23, and since C was twice as old as A at that time, C was 46. Adding four years back to C's past age gives C's present age as 50.