The quotient of two positive integers is 21. The difference between the larger
integer and this quotient is 21. What is the sum of the two integers?
Let's call the larger integer x and the smaller integer y.
We are given that the quotient of the two integers is 21, which means x/y = 21.
We are also given that the difference between the larger integer and this quotient is 21, which means x - (x/y) = 21.
Substituting x/y = 21 into the second equation, we get x - 21 = 21.
Solving for x, we find x = 42.
Substituting x = 42 into the first equation, we get 42/y = 21.
Solving for y, we find y = 2.
The sum of the two integers is x + y = 42 + 2 = 44. Answer: \boxed{44}.