Question
$\ \ \ \underline{\ \ \ \ \ \text{A}\ \ \ \text{A}{}\\\times \ \ \ \ \ \ \ \text{A}\ }\\\ \ \underline{\text{C}\ \ \text{ A}\ \ \ \text{ B}\ \ }$ and $B - A =1$.
✓
Answer
Here, $AA \times A$ is three digit number, whose unit’s digit is $B$,
Therefore $A$ can take values form $4$ to $9$ as $A = 0, 1, 2, 3$ give a single digit or a two-digit number.
Since, ten’s digit of the product is $A$, itself.
So, A cannot take values $4, 5, 6, 7$ and $8$ Hence, $A = 9$ and then $B = 1, C = 8$
Therefore $A$ can take values form $4$ to $9$ as $A = 0, 1, 2, 3$ give a single digit or a two-digit number.
Since, ten’s digit of the product is $A$, itself.
So, A cannot take values $4, 5, 6, 7$ and $8$ Hence, $A = 9$ and then $B = 1, C = 8$
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