Question

Replace A, B, C by suitable numerals.
$$\begin{gathered} \begin{array}{ccc}& A& B\\ \times & B& A\end{array} \\ \overline{\underline{\begin{array}{ccc}(B+1)& C& B\end{array}}} \end{gathered}$$

Answer 1

$A\times B=B\Rightarrow A=1$



In the question:
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

Required answer:

A=1, B=3, C = 0

or

A=1, B=4, C = 7