Question

A two digit number is such that the product of the digits is $16$. When $54$ is subtracted from the number, the digits are interchange. Find the number.

Answer 1

Let $y$ and $x$ be the right side and left side digits

$\left(x\right)\times \left(y\right)=16$ .......... $\left(1\right)$

$(10x+y)-54=(10y+x)$

$9x-54=9y$

$9(x-y)=54$

$x-y=6$

$x=6+y$

Substituting in $\left(1\right)$, we get

$y=2$

$x=8$

Hence required number is $82$.