# Find The Sum of Two Numbers ? If

If two numbers are in the ratio 2:3 and the ratio becomes 3:4 when 8 is added to both the numbers, then the sum of the two numbers is:

- 40
- 80
- 100
- 10

**Answer: (1) 40**

**Explanation:-
**The ratio of two numbers are 2 : 3.

Let the two number are 2 X & 3 X.

The ratio becomes 3:4 when 8 is added to both the numbers,

Then, (2 X + 8 ) / (3 X + 8) = 3 / 4

8 X + 32 = 9 X + 24 (By cross multiplication)

9 X – 8 X = 32 – 24

X = 8

Then, the numbers are 2 X = 2 x 8 = 16 & 3 X = 3 x 8 = 24

The sum of the numbers = 16 + 24 = 40

Hence, the answer is (1) 40.