Question

The sum of the digits number is $12$. If digits are reversed then number obtained is $54$ more than the original number. Find the original number.

Answer 1

Given sum of the digits is $12$

Let the digits in ones place be $x$

Hence the digit in tens place is $(12–x)$

The original number $=10(12–x)+x=120–9x$

Number formed by reversing the digits $=10x+(12–x)=9x+12$

Given that number formed by reversing the digits is $54$ greater than the original number.

$\Rightarrow 9x+12=(120–9x)+54=174–9x$

$\Rightarrow 18x=174–12=162$

$\therefore x=9$

The original number $=120–9x=120–9\times 9=120-81=39$