Question

A two digit number is four times the sum of the digits.It is also equal to $3$ times the product of digits.Find the number.

Answer 1

Consider the digit at tens place to be x and digit at ones place to be y. The two digit number is $10x+y$

$10x+y=4(x+y)$

$10x+y=4x+4y$

$6x=3y$

$y=2x$

$10x+y=3xy$ (Given)

Substituting $y=2x$,

$10x+2x=3x\times 2x$

$6x^2-12x=0$

$x(6x-12)=0$

$x=0$ or

$6x-12=0$

$x=2$

$y=4$

The two digit number is $24$