Question
Four years ago, the ratio of A’s age to B’s age was 5 : 3. Eight years from now, their ages will be in the ratio 3 : 2. Find B's present age.
Solution
Let 4 years ago: A = 5k, B = 3k. So present ages: A = 5k + 4, B = 3k + 4. Eight years from now: A = 5k + 12, B = 3k + 12 Given (fivek + 12):(3k + 12) = 3 : 2 (5k + 12) / (3k + 12) = 3/2 Cross-multiply: 2(5k + 12) = 3(3k + 12) 10k + 24 = 9k + 36 10k − 9k = 36 − 24 k = 12 Present ages: A = 5k + 4 = 5×12 + 4 = 64 years B = 3k + 4 = 3×12 + 4 = 40 years
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