Question

Find the values of $A,BandC$ in the following and give reasons for the steps involved. [AB] is a two digit number.

$AB$
$\times 5$
_____________
$CAB$

• A. $A=2,B=0,C=0$
• B. $A=5,B=0,C=2$
• C. $A=5,B=0,C=5$
• D. $A=5,B=2,C=2$

Answer 1

Answer: (B)

$A=5,B=0,C=2$

The multiplication of $B$ and $5$ is giving a number whose ones digit is $B$ again.
This is possible when $B=5$ or $B=0$
In case of $B=5$ , the product , $B\times 5=5\times 5=25$
2 will be carry for next step
We have $5\times A+2=\left[CA\right]$ which is possible for$A=2or7$
Then Multiplications will be

$\to 25\times 5=125$ (for $A=2$)
$\to 75\times 5=375$ (for $A=7$)
If $B=0$
$B\times 5=0\times 5=0$ There will be no carry in this step
In the next step , $5\times A=\left[CA\right]$
It is possible only when $A=5$ or $A=0$
But $A$ cannot be $0$ as $AB$ is a two digit number
Hence $A$ can be $5$ only
Then multiplication will be: $50\times 5=250$
Hence the possible value for $A,B$ and $C$ are:
$A=5,B=0$ and $C=2$