Question

If
$AB\times 5\underset{–}{}1BB\underset{–}{}$

then find the values of A and B.

Answer 1

Given : $AB\times 5=1BB$

In the units place, we have ones digit of $(B\times 5)=B$
$\Rightarrow B=5or0$

Now, if B = 5, in ones place column we have
$5\times 5=25$

5 in the ones place of the product and 2 carried over to tens place column.

Then, in tens place column,
$(5\times A)+2\left(carry\right)=155\times A=13$
This is not possible since ones place of $5\times A$ will always have either 0 or 5.
$\Rightarrow B\ne 5$
Hence, B = 0.

In the tens place, we have $A\times 5$ = 10.
Hence, A = 2

$20\times 5\underset{–}{}100\underset{–}{}$