The sum of two numbers is 40 and their difference is The ratio of the numbers is:

A 11:9

B 11:18

C 21:19

D 22:9

Correct Answer: Option A

Let x and y denote the two numbers and, without a loss of generality, let x > y.

Since the sum of the numbers is x + y

and

the difference is x - y,

we see that we have the system: x + y = 40 and

x - y = 4.

By adding these two equations: (x + y) + (x - y) = 40 + 4 ==> 2x = 44 ==> x = 22.

Then, since x + y = 40 implies y = 40 - x: y = 40 - x = 40 - 22 = 18.

Therefore, the two numbers are 22 and 18. so the ratio =22:18=11:9