The average of A and B is 20 years. If C were to replace A, the average would be 19 and if C were to replace B, the Average would be 21. What are the ages of A, B and C?

Let a, b, c are the ages of A, B and C respectively
a + b = 2 X 20 = 40 ...(1)
b + c = 2 x 19 = 38 ...(2)
c + a = 2 x 21 = 42 ...(3)
Adding all the 3 equalities
2a + 2b + 2c = 120
a + b + c = 60 --- (4)
From eq. (2) and (4)
a = 22
From eq. (1) and (4)
b = 18
From eq. (4)
c= 20
∴ Age of A = 22 years
Age of B = 18 years
Age of C = 20 years