Replace A, B, C by suitable numbers: (A,B)x(B,A)=(B+1)C,B

Question

Replace A, B, C by suitable numbers:

\(\begin{equation} \frac{ \begin{array}[b]{r} A\,\,B\\ \times\,\,\, B\,\,A \end{array} }{ (B+1) C\,B } \end{equation}\)

Answer 1

Here, we can observe that B × A = B

i.e. A = 1

Here,

First digit = B+1

Thus, 1 will be carried from 1+B² and becomes (B+1) (B² -9) B.

∴ C = B² -1

Now, all B, B+1 and B² -9 are one digit number.

This condition is satisfied for B=3 or B=4.For B< 3, B² -9 will be negative.

For B>3, B² -9 will become a two digit number.

For B=3, C = 32 - 9 = 9-9 = 0

For B = 4, C = 42 -9 = 16-9 = 7

Hence, A=1, B=3, C = 0 or A=1, B=4, C = 7