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 digit is added to the original number, if the sum is $66$. Find the number.

Answer 1

Let the tens digit be $x$ and the units digit be $y$.

So the number$=10x+y\dots \left(1\right)$

$x=2y\dots \left(2\right)$

After interchanging the digits we get

$10y+x$

Also,

$(10x+y)+(10y+x)=66$

$10x+y+10y+x=66$

$11y+11x=66$

$11(y+x)=66$

$y+x=\frac{66}{11}$

$y+x=6$

From equation $\left(1\right)x=2y$

So, $y+2y=6$

$3y=6$

$y=\frac{6}{3}$

$y=2$

And $x=2\left(2\right)=4$

Substitute in $\left(1\right)$

We get,

Number$=10x+y=10\left(4\right)+2$

Hence the number is $42$.