Question

Sum of the digits of a two digit number is $12$. The given number exceeds the number obtained by interchanging the digits by $36$. The given number is

• A. $81$
• B. $82$
• C. $83$
• D. $84$

Answer 1

The correct option is D $84$

Let one's digit be $x$.

Then, ten's digit $=12-x$
Number $=10(12-x)+x=120-10x+x=120-9x$
Number obtained by reversing the digits $=10\left(x\right)+12-x=12+9x$
According to the given condition, we have
$120-9x=12+9x+36$
$\Rightarrow 120-12-36=9x+9x$

$\Rightarrow 72=18x$

$\Rightarrow x=4$
So, the number $=120-9x=120-9\times 4=120-36=84$
Hence, the required number is $84$.