Question

The sum of the digits of a two-digit number is 7. If the number formed by interchanging the digits is less than the original number by 27, then find the original number.

Answer 1

$\text{Given, the sum of the digits of a two-digit number is 7.}$

$\text{Let the units digit of the}\text{original number be}x.$

$\text{Then, the tens digit of the}\text{original number is}7-x.$

$\text{The two-digit number}=10(7-x)+(1\times x)$
$=70-10x+x=70-9x$

$\text{When the digits are interchanged,}\text{the new number is}10\left(x\right)+1(7-x)=10x-x+7=9x+7$

$\text{New number = Original number - 27}$

$9x+7=70-9x-2718x=36x=2$

$\text{The tens digit}=7-x=7-2=5$

$\therefore \text{The original number is 52}$.