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Ratio of the present age of a father to that of the son is 7 : 1. After 5 years the ratio will become 4: 1. What is the difference (in years) in their present ages? Options : 10 20 30 40

Question

Ratio of the present age of a father to that of the son is 7 : 1. After 5 years the ratio will become 4: 1. What is the difference (in years) in their present ages?

Options : 10 20 30 40

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Solution

Let's denote the present age of the father as 7x and the present age of the son as x.

According to the problem, in 5 years, the ratio of their ages will be 4:1. This means that the father's age in 5 years (7x + 5) to the son's age in 5 years (x + 5) is 4:1.

We can set up the equation as follows:

(7x + 5) / (x + 5) = 4 / 1

Solving this equation will give us the value of x, which represents the son's present age. The father's present age is 7x.

The difference in their present ages is therefore 7x - x = 6x.

Let's solve the equation:

4(x + 5) = 7x + 5 4x + 20 = 7x + 5 3x = 15 x = 5

So, the difference in their present ages is 6x = 6*5 = 30 years.

So, the correct answer is 30.

This problem has been solved

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