# What will Ratio be Father and Son Ages? If

The sum of the ages of a father and his son is 100 now. 5 years age, their ages were in the ratio of 2:1. Find the Ratio of the ages father and son after 10 years from today.

- 4:3
- 5:3
- 3:5
- 10:7

**Answer: (2) 5 : 3**

**Explanation:-**

Let the age of father be X years & the age of his son is Y years.

The sum of the ages of father and his son = 100 years

Then, X + Y = 100 ……………………….. (1)

5 years ago the ratio of their ages = 2 : 1

Then, ( X – 5)/( Y – 5) = 2/1

By cross multiplication,

X – 5 = 2 Y – 10

X – 2 Y = -10 + 5

X – 2 Y = – 5 ………………………. (2)

Solve equation (1) & (2),

Then, X = 65 & Y = 35

Then, the age of father is 65 years & the age of his son is 35 years.

After 10 years,

The age of father is 65 + 10 = 75 & the age of his son is 35+ 10 = 45 years.

The ratio of the age of the father & the age of his son = 75 /45

= 5 : 3

Hence, the answer is (2) 5 : 3.