Question

The sum of a two digit number and the number obtained by interchanging the digits of the number is $121$. If digits of the number differ by $3$, find the number.

Answer 1

Let the two digit number is $10x+y$

According to the given question,

$(10x+y)+(10y+x)=121$

$\Rightarrow 11x+11y=121$

$\Rightarrow x+y=11........\left(1\right)$

Again, we know that,

$x-y=3........\left(2\right)$

By equation (1) and (2) to, we get

$x+y=11$

$\underset{–}{x-y=3}onadding$

$2x=14$

And

$x=7$

Put in the equation (1) and we get,

$x+y=11$

$7+y=11$

$y=4$

Hence, the number is

$=10x+y$

$=10\times 7+4$

$=74$

Hence, this is the answer.