Question

In an election between two candidates, the candidate who gets $30\%$ of the votes polled is defeated by $15,000$ votes. What is the number of votes polled for the winning candidate?

• A. $37,500$
• B. $30,000$
• C. $26,250$
• D. $11,250$

Answer 1

Answer: (C)

$26,250$

Let the number of votes $=X$

The number of votes of loosing candidate $=30\%$ of $X$

The number of votes of winning candidate $=70\%$ of $X$

Loosing candidate is defeated by $15000$ votes

$70\%$ of $X-30\%$ of $X=15000$

$\Rightarrow \frac{70X}{100}-\frac{30X}{100}=15000$

$\Rightarrow \frac{40X}{100}=15000$

$\Rightarrow X=37,500$ votes

The number of votes of winning candidate $=70\%$ of $X$

$=\frac{70}{100}\times 37500$

$=26,250$ votes