The difference between two numbers is 45. When 20% of the larger number is added to 35% of the smaller number, we get a sum of 31. What is the sum of the original numbers?

Correct option is A

Given:

The difference between two numbers is 45.

20% of the larger number added to 35% of the smaller number gives a sum of 31.

Solution:

Let the larger number be x and the smaller number be y.

The difference between the two numbers is 45:

x - y = 45

20% of the larger number added to 35% of the smaller number gives 31:

0.2x + 0.35y = 31

0.2(y + 45) + 0.35y = 31

0.2y + 9 + 0.35y = 31

0.55y + 9 = 31

0.55y = 22

y =$$\frac{22}{0.55} =$$​40

x = y + 45 = 40 + 45 = 85

Sum of the numbers = x + y = 85 + 40 = 125

Thus, the sum of the original numbers is 125.