Question
The present age of a father is 5 times the age of his
son. In 6 years, the father's age will be 4 times the age of his son. How many years ago was the father's age 7 times the son's age?Solution
Let the present age of the son be x years. Then the father's age is 5x years. In 6 years, the father's age will be 5x + 6 and the son's age will be x + 6. Given: 5x + 6 = 4(x + 6). 5x + 6 = 4x + 24. x = 18 years. So, the father's current age is 5 * 18 = 90 years. Let y years ago, the father's age was 7 times the son's age. 90 - y = 7(18 - y) 90 - y = 126 - 7y 6y = 36 → y = 6 years.
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