Two numbers are in the ratio of 2 : 3. If each number is increased by 4 the…

Step-by-Step Solution
Define the numbers: Since the ratio of the two numbers is 2:3, let the numbers be 2x and 3x.

Set up the equation: If each number is increased by 4, the ratio becomes 5:7. We can write this as a proportion:
(2x + 4) / (3x + 4) = 5 / 7

Cross-multiply to solve for x:
7 * (2x + 4) = 5 * (3x + 4)
14x + 28 = 15x + 20

Isolate x:
28 - 20 = 15x - 14x
x = 8

Find the two numbers:

First number: 2x = 2 * 8 = 16

Second number: 3x = 3 * 8 = 24

Calculate the sum:
Sum = 16 + 24 = 40