In a local election between two candidates, one candidate got 55% of the total valid votes and was declared as winner.15% of the votes were invalid. If the total number of votes polled were 15200, what were the valid votes of the loser :
- 6840
- 5800
- 5814
- 6216
The Correct Option is C
Solution and Explanation
To find the valid votes of the losing candidate in the election, we will follow these steps:
Calculate the number of invalid votes.
The total number of votes polled is 15,200 and 15% of these votes were invalid.
Therefore, the number of invalid votes is calculated as:
\(= \left(\frac{15}{100}\right) \times 15200 = 2280\)
Determine the number of valid votes.
Valid votes = Total votes polled - Invalid votes
\(= 15200 - 2280 = 12920\)
Find the number of valid votes received by the winning candidate.
The winning candidate received 55% of the total valid votes. Therefore,
\(= \left(\frac{55}{100}\right) \times 12920 = 7106\)
Calculate the number of valid votes received by the losing candidate.
Since the sum of the votes for both candidates must equal the total valid votes, we calculate the votes for the loser as:
Valid votes for loser = Total valid votes - Valid votes for winner
\(= 12920 - 7106 = 5814\)
Thus, the number of valid votes received by the losing candidate is 5814.
Option 5814 is the correct choice.
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