Two numbers are in the ratio 2 : 7. If the first number is increased by 14 and the second number is decreased by 6 , then the ratio becomes 4 : 3. What is the sum of the original two numbers?

Correct option is B

Given:

Two numbers are in ratio 2:7

First number is increased by 14

Second number is decreased by 6

New ratio = 4:3

Formula Used:

Ratio and Proportions

Solution:

Let the ratio be 2x and 7x

According to question:

​$$\frac{2x+14}{7x-6} = \frac{4}{3}$$​​

3(2x+14)= 4(7x-6)

6x+42 = 28x - 24

42+24 = 28x -6x

66 = 22x

x= 3

Sum of original numbers = 2x+7x = 9x = $$9 \times 3$$​ = 27