Question

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

• A. $92$
• B. $91$
• C. $90$
• D. None of these

Answer 1

Answer: (A)

Let ten's place digit number $=x$ and unit's place digit number $=y$
$\therefore$ Number $=10x+y$
According to the question,
$xy=18$........(i)
$10x+y-63=10y+x$
$9x-9y=63\Rightarrow x-y=7$.........(ii)
${(x+y)}^2={(x-y)}^2+4xy$
$=49+72=121$
$x+y=11$
From equation (ii) and (iii) we get,
$x=9,y=2$
$\therefore$ Number $=92$