Question
The present ages of A and B are in the ratio 5 : 7.
After 6 years, the ratio of their ages will be 4 : 5. Find A's present age.Solution
Let present ages be: A = 5x, B = 7x After 6 years: A = 5x + 6 B = 7x + 6 Given: (5x + 6) : (7x + 6) = 4 : 5 So, (5x + 6)/(7x + 6) = 4/5 Cross-multiply: 5(5x + 6) = 4(7x + 6) 25x + 30 = 28x + 24 Bring like terms together: 28x − 25x = 30 − 24 3x = 6 x = 2 Present ages: A = 5x = 5 × 2 = 10 years B = 7x = 7 × 2 = 14 years Answer: A = 10 years.
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