Question

When a number is subtracted from a number with digits as the reverse of the original number, we get 27. The sum of the digits is 7. The original number is

Answer 1

Let the number is $xy.$
This number can be represented as $10x+y.$
The number with digits as the reverse to the original number is $yx.$
It is equaivalent to $10y+x.$

When the number is subtracted from the number with digits as the reverse of the original number, we get 27.
$\Rightarrow yx-xy=27$
$\Rightarrow 10y+x-(10x+y)=27$
$\Rightarrow 10y+x-10x-y=27$
$\Rightarrow 9y-9x=27$
$\Rightarrow 9(y-x)=27$
$\Rightarrow y-x=3...\left(a\right)$

Also, the sum of the digits is 9.
$\Rightarrow x+y=7...\left(b\right)$

Add (a) and (b) to eliminate $x.$
$y-x+x+y=3+7$
$\Rightarrow 2y=10$
$\Rightarrow y=5$

Substituting $y$ in (a) we get,
$5-x=3$
$\Rightarrow x=2$

$\therefore$ The original number $xy$ is $25.$