Question

A two- digit number contain the smaller of the two digits in the place. The product of the digits is $40$ and the difference between the digits is $3$.Find the number.

Answer 1

Let the two digit number will be first $x$ and second is $y$

The two digit number is $10x+y$

$xy=40$

$x=\frac{40}{y}$

$x-y=3$ --- (i)

$\frac{40}{y}-y=3$

$y^2+3y-40=0$

$y^2+8y-5y-40=0$

$y(y+8)-5(y+8)=0$

$y=5$ as it cannot be $-8$

From (i)

$x-5=3⟹x=8$

$⟹$ The two digit number is $10x+y=10\left(8\right)+5=85$