Question

$n$ is a two digit number. $P\left(n\right)$ is the product of the digit of $n$ and $S\left(n\right)$, is the sum of the digits of $n$. If $n=P\left(n\right)+S\left(n\right)$ then find the units digit of $n$.

Answer 1

A] Let a,b be tens & unit digits of n

Then n = 10 a + b

p(n) + s(n) = 10 a + b

= a b + a+b = 10 a +b

= a b = 9 a

$\therefore b=9$ as $a\ne 0$

$\therefore$ units digit is 9