Question

Find the two-digit number if the number of its units exceeds by $2$ the number of its tens and the product of the required number, by the sum of its digits is equal to $144$.

Answer 1

Let the tenth digit be $10x$

Then, unit's unit $=x+2$

Number $=10x+(x+2)=11x+2$

Sum of digits $=x+x+2=2x+2$

$(11x+2)(2x+2)=144$

$\Rightarrow 11x^2+26x-140=0$

$\Rightarrow 11x^2+13x-70=0$

$\Rightarrow (x-2)(11x+35)=0$

$\Rightarrow x=2$

Hence the required number is $(11\times 2)+2=24$.