KVPY 2019 SA Exam Previous Papers

three digit number $\overline{\mathit{a}\mathit{b}\mathit{c}}$, such that
$\frac{\mathit{b}+\mathit{c}}{2}=\mathit{b}\mathit{c}$
the above relation is true if $\mathit{b}=\mathit{c}=0$
And if neither $\mathit{b}$ nor $\mathit{c}$ is zero, then $\frac{1}{\mathit{b}}+\frac{1}{\mathit{c}}=2,$
and $\mathit{b},\mathit{c}\in \left\{1,2,3,4,5,6,7,8,9\right\}$
Then $\mathit{b}=\mathit{c}=1$
and $\mathit{a}\in \left\{1,2,3,4,5,6,7,8,9\right\}$
So, total number of such three digit number are $2\times 9=18$