Question

Find the values of the letters in the following and give reasons for the steps involved.
$AB\underset{–}{\times 3}\underset{–}{CAB}$

Answer 1

In the given problem, if $B\times 3$ has to end with $B$, then $B$ has to be either $0$ or $5$, because only $0$ or $5$, when multiplied by $3$, will give the same number.

If $B=5$, then there will be a carry-over, which will not give the next product as $CA$.

Thus, $B=0.$

Also, $A\times 3$ ends with $A$, so $A=5$.

And $3\times 5=15$

$\therefore C=1$

Hence, $A=5,B=0andC=1.$