Question

A two digit number is such that the product of its digits is 18. When 63 is subtracted from the number, the digits interchange their places. Find the number.

Answer 1

Let the tens digit be x. Then, the units digits $=\frac{18}{x}$

$\therefore$ Number $=10x+\frac{18}{x}$

and, Number obtained by interchanging the digits $=10\times \frac{18}{x}+x$

$\therefore (10x+\frac{18}{x})-(10\times \frac{18}{x}+x)=63$

$\Rightarrow 10x+\frac{18}{x}-\frac{180}{x}-x=63$

$\Rightarrow 9x-\frac{162}{x}-63=0$

$\Rightarrow 9x^2-63x-162=0$

$\Rightarrow x^2-7x-18=0$

$\Rightarrow (x-9)(x+2)=0\Rightarrow x=9or,x=-2$

But, a digit can never be negative. So, x = 9

Hence, the required number $=10\times 9+\frac{18}{9}=92$