Question : In an election between 2 candidates, the winning candidate gets 2940 valid votes, while the losing candidate gets 40% of the valid votes. If 2% of the votes polled were declared invalid, then what is the total number of votes polled?
Option 1: 4500
Option 2: 5000
Option 3: 6000
Option 4: 5500
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Correct Answer: 5000
Solution : Let $100x$ be the total number of votes. 2% of votes were invalid = $2x$ The number of votes valid = $100x - 2x = 98x$ According to the question, $\frac{60}{100}\times 98x=2940$ ⇒ $\frac{3}{5}\times 98x=2940$ ⇒ $98x=980\times 5$ ⇒ $x=50$ The total number of votes polled $=100x=100\times 50= 5000$ votes Hence, the correct answer is 5000.
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