The ratio between two numbers is 19 : 24. If each number is reduced by 36, the ratio becomes 3 : 4. Find the sum of the numbers.

Correct option is A

Given:

Original ratio = 19 : 24
After reducing each number by 36, new ratio = 3 : 4

Solution:
Let the two numbers be 19x and 24x
After reducing by 36, the new ratio is:

​$$\frac{19x - 36}{24x - 36} = \frac{3}{4}$$​​

4(19x - 36) = 3(24x - 36)

76x - 144 = 72x - 108

4x = 36

x = 9

First number = 19x = 171,

Second number = 24x = 216

Then, Sum = 171 + 216 = 387