Question

The sum of the digits of a two-digit number is $15$.If the number formed by reversing the digits is less than the original number by $27$,find the original number.

Answer 1

Let the unit's place$=x$

Then the ten's place$=15-x$

$\therefore$ original number$=10(15-x)+x=150-10x+x=150-9x$

By reversing the digits, we get

New number$=10x+(15-x)=10x+15-x=9x+15$

According to the problem,

original number$-$New number$=27$

$\Rightarrow 150-9x-9x-15=27$

$\Rightarrow -18x+135=27$

$\Rightarrow -18x=27-135=-108$

$\Rightarrow x=\frac{-108}{-18}=6$

Hence original number$=150-9x=150-9\times 6=150-54=96$