10\% of the voters did not cast their vote in an election between two candidates. 10\% of the votes polled were found invalid. The successful candidate got 54\% of the valid votes and won by a majority of 1620 votes. The number of voters enrolled on the voters' list was
(a)25000
(b)33000
(c)35000
(d)40000
Answer
Answer (as printed): A
Explanation
Let the total number of voters be $x$. Then, votes polled $=90 \%$ of $x$. Valid votes $=90 \%$ of (90\% of $x$ ). $\therefore 54 \%$ of $[90 \%$ of (90\% of $x)]-46 \%$ of [90\% of (90\% of x)] = 1620 $$\begin{aligned} & \Leftrightarrow \quad 8 \% \text { of }[90 \% \text { of }(90 \% \text { of } x)]=1620 \\ & \Leftrightarrow \quad \frac{8}{100} \times \frac{90}{100} \times \frac{90}{100} \times x=1620 \\ & \Leftrightarrow \quad x=\left(\frac{1620 \times 100 \times 100 \times 100}{8 \times 90 \times 90}\right)=25000 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.