Two numbers are in the ratio 2 : 4. If the first number is increased by 4 and the second number is decreased by 14, then the ratio becomes 8 : 5. What is the sum of the original two numbers?

Correct option is D

Given:

The ratio of two numbers is 2 : 4

When the first number is increased by 4 and the second number is decreased by 14, the new ratio becomes 8 : 5

Solution:

Let the two numbers be 2x and 4x

According to the question;

​$$\frac{2x + 4}{4x – 14} = \frac{8}{5}$$​​

5(2x + 4) = 8(4x – 14)

10x + 20 = 32x – 112

10x – 32x = -112 – 20

-22x = -132

x = $$\frac{132}{22}$$​​

x = 6

Now,

the numbers be

2x = 2×6 = 12

4x = 4×6 = 24 

Thus, sum of numbers be 12 + 24 = 36