Adding all the digits according to their places,

20 + B + 10A + B = 80 + A

9A + 2B = 60

9A = 60-2B

Since A and B both are whole numbers, 60-2B should be divisible by 9.

60-2B = 54 so B = 3.

Substituting B = 3 in 9A + 2B = 60,

we get A = 6.