Question 53

The sum of the present ages of a father and his son is 78 years. After five years, the ratio of their ages becomes 7 : 4. What is the present age (in years) of the father?

Solution

Given,

Sum of present ages of father and son is 78 and their ratio after 5 years is 7:4

let the age of father and son after 5 years be 7x and 4x

sum of the present ages can be written as,

(7x-5) + (4x-5) = 78

7x + 4x - 10 = 78

11x - 10 = 78

11x = 88

x = 8

The age of father after 5 years is $${7}\times{8}$$ = 56

therefore the present age of father is 56 - 5 = 51

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