Question
The ratio of the present ages of A and B is 3 : 5. After
8 years, the ratio of their ages will be 7 : 11. Find their present ages.Solution
Let present ages be: A = 3x, B = 5x After 8 years: A = 3x + 8 B = 5x + 8 Given: (3x + 8) / (5x + 8) = 7 / 11 Cross-multiply: 11(3x + 8) = 7(5x + 8) 33x + 88 = 35x + 56 35x − 33x = 88 − 56 2x = 32 ⇒ x = 16 So A = 3x = 3 × 16 = 48 years B = 5x = 5 × 16 = 80 years Check after 8 years: A = 56, B = 88 ⇒ 56 : 88 = 7 : 11 (correct).
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