Question

A two-digit number is four times the sum and three times the product of its digits. Find the number.

Answer 1

Let the two digit number be $10y+x$

it is given that $10y+x=4(x+y)...\left(1\right)$

and $10y+x=3xy...\left(2\right)$

So, $10y+x=4x+4y$ and

$\Rightarrow 63y=3x$

$\Rightarrow 2y=x$

Substituting in (2)

$10y+2y=6y^2$

$\Rightarrow 12y=6y^2$

$\Rightarrow 2=y$

$\Rightarrow x=4$

$\therefore$ The number is $10\times 2+4=24$