Question : In an election between two candidates, the difference between the candidates who won and lost was 2,500 votes. The candidate who won got 75% of the votes, and there were no invalid votes. The total number of votes polled by the losing candidate was:
Option 1: 1875
Option 2: 5000
Option 3: 1250
Option 4: 3750
Correct Answer: 1250
Solution :
Let V be the total number of votes polled.
The winning candidate received 75% of the votes, which is 0.75V.
⇒ The losing candidate received the remaining 25% of the votes, which is 0.25V.
The difference between the votes of the winning and losing candidates is 2,500.
⇒ 0.75V - 0.25V = 2,500
⇒ 0.5V = 2,500
⇒ V = $\frac{2,500}{0.5}$
⇒ V = 5,000
⇒ The losing candidate received 0.25 × 5,000 = 1,250 votes
Hence, the correct answer is 1250.
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