Question

The sum of two digits number and the number obtained by reversing the order of the digit is $165$. If the digits are differ by $3$, find the original number.

Answer 1

Let the two-digit no. be $xy$

No. obtained by reversing it is $yx$

Sum$=165$

$xy+yx=165$

$10x+y+10y+x=165$

$11x+11y=165$

$x+y=\mathrm{15............}1$

Given that $x-y=\mathrm{3..............2}$

Adding both equations $1+2$

$2x=18$

$x=9,y=6$

$\therefore$ No. is $96$