Two numbers are in the ratio 2:3. If 5 is added to both the numbers the ratio becomes 5:7. Find the bigger number

Given:
The ratio of two numbers is 2:3.
If 5 is added to both numbers, the ratio becomes 5:7.

The ratio of two numbers is 2:3. = 2x and 3x

If 5 is added to both numbers, the ratio becomes 5:7.

Then,

​$$\frac{2x + 5}{3x + 5} = \frac{5}{7}$$

7(2x + 5) = 5(3x + 5)

14x + 35 = 15x + 25

14x - 15x = 25 - 35

​​-x = -10

x = 10

The bigger number is 3x = $$3 \times 10$$​ = 30.

Thus, the correct answer is (c).