# Find the Ratio Between Younger Brother and Elder Brother

The sum of the ages of two brother, having a difference of 8 years between them, will double after 10 years, What is the ratio of the age of the younger brother to that of the elder brother ?

- 8:9
- 10:13
- 7:11
- 3: 7

**Answer: (4) 3:7**

**Explanation:-
**Let the age of elder brother be x years and smaller brother be y years.

Then, According to first condition,

x – y = 8 —– (i)

and sum is x+y

Again, it is given that the sum of their ages will double after 10 years. The equations thus formed is

2(x+y) = (x+10) + (y+10)

Thus, 2x + 2y = x+y+20

x+y=20 —— (ii)

adding (i) and (ii), we get

2x = 28

x = 14 years

and y is 14- 8 = 6 years

Therefore, ratio of younger to elder brother is 6/14 = 3/7

Then, the ration of the age of the younger brother to that of the elder brother = 3 : 7.

Hence, the answer is (4) 3 : 7.