Lets work backward -

What we know XY is two digit and X+Y+1=D which is one digit i.e. 9 or less.

Lets assume D is 9 then X+Y=8 such means X*Y can be (6,2)12, (5,3)15, (4,4)16

1) Now if X*Y is 12 (we know D is 9)

=>A+B+C=3 not possible

2) Now if X*Y is 15 (we know D is 9)

=>A+B+C= 6 i.e. A=1, B=2, C=3 (a solution)

3) Now if X*Y is 16 (we know D is 9)

=>A+B+C=7 i.e. A=1, B=2, C=4 (a solution)

Possible Solutions are

**1) A=1, B=2, C=3, D=9 **

2) A=1, B=2, C=4, D=9