Question

A two digit number is such that the product of its digits is $12$. When $36$ is added to the number, its digit are reversed. Find the number.

Answer 1

Let the unit's digit in the number be $x$, then as product of digits is $12,$ the ten's digit in the number is=$12x$.

Hence, the value of the number is $10\times 12x+x=120x+x$

On reversing the digits, unit's digit becomes ten's digit and ten's digit becomes unit's digit and its value will become$=10x+12x$

It is apparent that $(10x+12x)\ge 120x+x$ by $36$

Hence,

$10x+12x=120x+x+36$

or

$9x=120-12x+36$

or

$9x=108x+36$

dividing each term by $9$ we get

$x=12x+4$

multiply each by$x$ to get

$x^2=12+4xorx2-4x-12=0$

i.e. $x^2-6x+2x-12=0$

or

$x(x-6)+2(x-6)=0$

i.e. $(x+2)(x-6)=0$

Hence, $x=-2$ or $x=6$

As, we cannot have negative number in units place

Hence, 6 is in unit's place and in ten's place we have $126=2$

and number is $26$