Given are two numbers whose ratio is 7:3. If 2 is added to each of them, their ratio becomes 2:1. What is the sum of these two numbers?

The sum of the two numbers is 20.

Let them be 7x and 3x.

(7x + 2)/(3x + 2) = 2/1 gives 7x + 2 = 6x + 4.

x = 2, so the numbers are 14 and 6.

Sum = 14 + 6 = 20.