Question

The difference of the number consisting of two digits and the number formed by interchanging the digit is always divisible by

• A. $5$
• B. $7$
• C. $9$
• D. 11

Answer 1

Answer: (C)

$9$

A two digit number can be written as $10x+y$
where $x$ is the digit at ten's place and $y$ is the digit at one's place.

On interchanging the digits the number formed $=10y+x$
$Difference=10x+y-(10y+x)=9x-9y=9(x-y)$
$\Rightarrow$ Given difference is always divisible by 9.