5 years hence, the age of a man shall be 3 times the age of his son while 5 years earlier the age of the man was 7 times the age of his son. The present age of the man is ______.

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5 years hence, the age of a man shall be 3 times the age of his son while 5 years earlier the age of the man was 7 times the age of his son. The present age of the man is 40 years. Explanation: Let the man’s present age = x and his son’s = y. From 5 years hence: x + 5 = 3(y + 5) $\Rightarrow$ x – 3y = 10 From 5 years earlier: x – 5 = 7(y – 5) $\Rightarrow$ x – 7y = –30 Subtracting gives 4y = 40 $\Rightarrow$ y = 10 So, x = 3 $\times$ 10 + 10 = 40 years

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