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-

Question: 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-

Solution:
Let, the numbers be 2x and 3x respectively.

ATQ,
(2x + 8)/(3x + 8) = 3/4
⇒ 9x + 24 = 8x + 32
⇒ 9x - 8x = 32 - 24
⇒ x = 8

∴ Sum of numbers = 2x + 3x
= 5x
= 5 × 8
= 40