a man is twice as old as his son. Five years ago the ratio of their ages was 9:4.Find the sum of their ages

75years

Explanation:

Let the Father's age be represented by 2x

Let the Son's age be represented by x

Five years ago;

Man's age will be = 2x - 5

Son's age will be = x - 5

If the ratio of their ages five years ago was 9:4, then;

2x - 5/x-5 = 9/4

4(2x - 5) = 9(x - 5)

8x - 20 = 9x - 45

- Collect like terms

-20 + 45 = 9x - 8x

25 = x

Hence, the son's age = 25 years

If x = 25, the father's age (2x) will be 2 × 25 = 50years

The sum of their ages will be = 25years + 50years = 75years

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