Question

The units digit of a two-digit number is greater than its tens digit by $2$ and the product of that number by the sum of its digits is $144$. Find the number.

Answer 1

Let $n(a,b)$ be two digit number.

$n(a,b)=10a+b$

Units digit=ten's digit+2

$b=a+2$

$\text{number times sum of digits}=144$

$(10a+b)(a+b)=144$

$(11a+2)(2a+2)=144$ $(\because b=a+2)$

11a^{2}+13a+2=72$

$11a^2+13a-70=0$

$11a^2+35a-22a-70=0$

$(11a+35)(a-2)=0$

$\therefore a=2,b=4$

$\therefore 24$ is the required number.