In an election, 30\% of the voters voted for candidate A whereas 60\% of the remaining voted for candidate B. The remaining voters did not vote. If the difference between those who voted for candidate A and those who did not vote was 1200, how many individuals were eligible for casting vote in that election?
(a)10,000
(b)45,000
(c)60,000
(d)72,000
Answer
Answer (as printed): C
Explanation
Let the number of persons eligible to vote be $x$. Then, voters who voted for $\mathrm{A}=30 \%$ of $x$. Voters who voted for $\mathrm{B}=60 \%$ of (70\% of $x$ ) $$=\left(\frac{60}{100} \times \frac{70}{100} \times 100\right) \% \text { of } x=42 \% \text { of } x .$$ Voters who did not vote $=[100-(30+42)] \%$ of $x=28 \%$ of $x$. $$\begin{aligned} & \therefore 30 \% \text { of } x-28 \% \text { of } x=1200 \\ & \Leftrightarrow 2 \% \text { of } x=1200 \Leftrightarrow x=\left(\frac{1200 \times 100}{2}\right)=60000 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.