Question

Sum of the digits of a two digit number is $9$. When we interchange the digits, it is found that the resulting new number is greater than the original number by $27$. What is the two digit number?

• A. $31$
• B. $33$
• C. $37$
• D. $36$

Answer 1

The correct option is D $36$

Let the unit digit be $x$.

Then, ten's digit $=9-x$
So, number $=10(9-x)+x=90-10x+x=90-9x$
On interchanging the digits, new number $=10x+9-x=9+9x$
According to the given condition, we have
$9x+9=90-9x+27$
$\Rightarrow 9x+9x=90+27-9$

$\Rightarrow 18x=108$

$\Rightarrow x=6$
So, unit digit $=6$ and ten's digit $=3$
Therefore, the number is $36$.