Answer
The original number of members is $50$ person
Work Step by Step
$\textbf{i}\hspace{0.3cm}$ If the original number of people is $x$. So the cost per person is $900 / x$.
$\textbf{ii}\hspace{0.3cm}$ Let the new number of people is $x-5$. So cost per person is $900 / (x-5)$ .
$\textbf{iii}\hspace{0.3cm}$ Hence the cost per person after $5$ people withdrew is $\$2$ more than the original cost
$\Rightarrow 900 / (x - 5) = (900 / x ) + 2$
$\Rightarrow x(x-5)\bigg(900 / (x - 5)\bigg) = x(x-5)\bigg(900 / x \bigg) + 2x(x-5)$
$\Rightarrow 900x = 900(x-5) + 2x(x-5)$
$\Rightarrow 900x = 900x-4500 + 2x^2-10x$
$\Rightarrow 2x^2-10x-4500 =0$
$\Rightarrow x^2-5x-2250 =0$
$\Rightarrow (x+45)(x-50) =0$
$\Rightarrow (x+45) =0$ or $(x-50) =0$
$\Rightarrow x=-45 \hspace{0.3cm}{\color{red}{reject}}$
or $x=50$
i.e The original number of members is $50$ person
