Question

There is a number which is equal to $4$ times the sum of its digits. If $27$ is added to the number, the number's digits get reversed. Find the number

Answer 1

Let $x$ be the first digit of to digit number

and $y$ be second digit of two digit number.

Therefore, two digit number so formed is $10x+y$.

As per the given condition,

$10x+y=4(x+y)$

$\Rightarrow 10x+y=4x+4y$

$\Rightarrow 6x=3y$

$\Rightarrow y=2x$

Now, if $27$ is added to the number, the number is reversed.

$10x+y+27=10y+x$

$\Rightarrow 10x+2x+27=10\left(2x\right)+x$

$\Rightarrow 12x+27=20x+x$

$\Rightarrow 12x+27=21x$

$\Rightarrow 27=9x$

$\Rightarrow x=3$

Therefore, $y=2x=2\times 3=6$

Therefore, the number is $36$.