Question

To win an election, a candidate needs $\frac{3}{4}$ of the votes cast. If, after $\frac{2}{3}$ of the votes have been counted, a candidate has $\frac{5}{6}$ of what he needs, then what part of the remaining ratio does he still need?

• A. $\frac{1}{10}$
• B. $\frac{1}{8}$
• C. $\frac{1}{4}$
• D. $\frac{3}{8}$

Answer 1

The correct option is D $\frac{3}{8}$

Let us assume that the total no. of votes be $x$.
Therefore, a candidate needs $\frac{3x}{4}$ votes.
However, $\frac{2x}{3}$ votes have already been counted, so $\frac{x}{3}$ votes are still to be counted.
The candidate has $\frac{5}{6}$ of $\frac{3x}{4}$.
$=\frac{5\times 3x}{6\times 4}$

$=\frac{5x}{8}$
Hence, he still needs
$=\frac{3x}{4}-\frac{5x}{8}$

$=\frac{x}{8}$

The total no of remaining votes $=\frac{x}{3}$

Hence, the fraction of the remaining votes he needs to win is $\frac{3}{8}$.