Question

The tens digits of a two-digit number exceeds the units digit by 5. If the digits are reversed, the new number is less by 45. If the sum of their digits is 9, find the numbers.

Answer 1

Let the digit in the units place be $x$

Hence the digit in the tens place is $(x+5)$

The original number $=10(x+5)+x=11x+50$

Number formed by reversing the digits $=10x+(x+5)=11x+5$

Given that:- $(11x+50)+(11x+5)=99$

$\Rightarrow 22x+55=99$

$\Rightarrow 22x=99-55=44$

$\Rightarrow x=2$

$\therefore$ Original number $=11x+50=11\left(2\right)+50=72$

Hence the original number is $72$.

Hence the correct answer is $72$.