Question

The sum of a two digit number and the number obtained by interchanging the digits of the number is $121$. If the digits of the number differ by $5$, then numbers are _______.

• A. $62,26$
• B. $38,83$
• C. $42,24$
• D. $37,73$

Answer 1

Answer: (B)

$38,83$

Let the digits of number be $x$ and $y$, $x$ being on Ten's place and $y$ on One's place.

$\Rightarrow$ Number is $10x+y$

Number formed by interchanging the digits is $10y+x$

Given that the sum of both these numbers is $121$

$\therefore 11x+11y=121$

$x+y=\mathrm{11......}\left(1\right)$

Also given that the difference of digits is $5$, i.e. $y-x=\mathrm{5......}\left(2\right)$

Adding $\left(1\right)$ and $\left(2\right)$ we get, $y=8$ and $x=3$

$\therefore$ Numbers are $38$ and $83$