The average age of A and B is 20 years. If A is to be replaced by C, the average would be 19 years. The average age of C and A is 21 years. The ages of A, B and C in order (in years) are:

22, 18, 20

 average age of A and B is 20 years 

 A + B = 40 years        ----- ( 1) 

The average age of C and A is 21 years

  C + A = 42 years       ------ ( 2) 

 if A is replaced by C . then , average of B  and C is 19 years. 

  B +  C = 38 years       ------ ( 3 ) 

adding equation, 1 + 2 + 3 

   A+  B +  C = 60 years 

( A + B + C ) - ( A + B ) = 60 - 40  

 C= 20  years

( A + B + C ) - ( B + C ) = 60 - 38 

A =  22 years 

( A + B + C ) - ( A + C ) = 60 - 42 

 B = 18 years