Question

In a two digit number, digit at the ten's place is twice the digit at unit's place. If the number obtained by interchanging the digits is added to the original number, the sum is $66.$ Find the number.

Answer 1

Let the two digit number be $XY$

given that $x=2y$

$\Rightarrow$ number $=\left(2y\right)y$

$=y<5$

number obtained by interchanging digits $y\left)\right(2y)$

given ,Sum $=\left(10\right(2y)+y]+\left[10\right(y)+2y)]=66$

$\Rightarrow 21y+12y=66$

$\Rightarrow 33y=66$
$y=2$

$2y=4$

$\therefore$ the number id $\left(2y\right)y=42$