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5 years ago a man was 7 times as old as his son. 5 years from now he will be 3 times as old as his son. What was his age two years ago?

5 years ago a man was 7 times as old as his son. 5 years from now he will be 3 times as old as his son. What was his age two years ago? Correct Answer 38 years and 8 years

Given:

5 years ago, A man was 7 times = As his son

Now in 5 years, A man will be = 3 times as old as his son

Calculation:

Let five years ago, son age be x and father age be 7x respectively

Present age of son = (x + 5)

Present age of father = (7x + 5)

5 years later, son age = (x + 5 + 5) = (x + 10)

5 years later, father age = (7x + 5 + 5) = (7x + 10)

According to the question

⇒ (7x + 10) = 3(x + 10)

⇒ 7x + 10 = 3x + 30

⇒ 7x – 3x = 30 – 10

⇒ 4x = 20

⇒ x = (20/4)

⇒ x = 5

Present age of son = (x + 5) = (5 + 5)

⇒ 10

Present age of father = (7x + 10) = (7 × 5 + 5)

⇒ 40

Now,

Son age two years ago = (10 – 2) = 8 years

Father age two years ago = (40 – 2) = 38 years

∴ The required age is 38 years and 8 years

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