Question

The sum of two-digit numbers and the number obtained by reversing the order of the digit is $121$. Find the number, if the digits differ by $3$.

• A. $47$ or $74$
• B. $36$ or $63$
• C. $67$ or $76$
• D. $94$ or $49$

Answer 1

The correct option is A $47$ or $74$

Let the two digit number be $10x+y$
On reversing its digits, we get the number $10y+x$
Given, $(10x+y)+(10y+x)=121$
$11x+11y=121$
=> $x+y=11$ --- $\left(1\right)$
Given, $x-y=3$ -- $\left(2\right)$
Adding $\left(1\right)$ and $\left(2\right),$ we get
$2x=14$ => $x=7$
Substituting $x=7$ in the equation $\left(2\right)$, we get $7-y=3\Rightarrow y=4$
Hence, the number is $74$ or $47$