Question
The current ages of A and B are in the ratio of 4:7. Six
years from now, the ages of B and C will be in the ratio of 2:3. If the average of the present ages of A, B, and C is 44 years, what is the difference between the current ages of A and C?Solution
Let the present ages of A and B are 4x years and 7x years respectively. Age of B after six years = 7x + 6 years Age of C after six years = (7x + 6) × 3/2 = ‘10.5x + 9’ years Present age of C = 10.5x + 9 – 6 = ‘10.5x + 3’ years According to question: 4x + 7x + 10.5x + 3 = 3 × 44 21.5x + 3 = 132 21.5x = 129, x = 6 So the present age of A = 4 × 6 = 24 years Present age of C = 10.5 × 6 + 3 = 63 + 3 = 66 years So the desired difference = 66 – 24 = 42 years
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