The ratio of the present age of X to that of Y is 4 : 5. k (less than 10) years ago, this ratio was 1 : 2. How many values of k are possible if the ages are expressed in complete years ?

Explanation

Let present ages be 4x and 5x. Given (4x - k) / (5x - k) = 1 / 2, which gives 8x - 2k = 5x - k, meaning 3x = k. For x to be an integer (complete years) and k < 10, the positive multiples of 3 are 3, 6, and 9. Thus, 3 values are possible.

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