In an election contested between two candidates, winner beat the loser by 5040 votes. If out of total votes cast, 16% were declared invalid and winner received 75% of the total valid votes, then find the number of invalid votes cast. Options 1520 1920 1740 1280
Question
In an election contested between two candidates, winner beat the loser by 5040 votes. If out of total votes cast, 16% were declared invalid and winner received 75% of the total valid votes, then find the number of invalid votes cast.
Options 1520
1920
1740
1280
Solution
Let's solve this step by step:
Step 1: Let's assume the total number of votes cast in the election is 'x'.
Step 2: According to the problem, 16% of the total votes were declared invalid. So, the number of invalid votes is 16% of 'x', which is 0.16x.
Step 3: The valid votes are the total votes minus the invalid votes, which is x - 0.16x = 0.84x.
Step 4: The winner received 75% of the total valid votes, which is 0.75 * 0.84x = 0.63x.
Step 5: The loser received the remaining valid votes, which is 0.84x - 0.63x = 0.21x.
Step 6: According to the problem, the winner beat the loser by 5040 votes. So, 0.63x - 0.21x = 5040. Solving this equation gives x = 12000.
Step 7: Substituting x = 12000 into the equation for the number of invalid votes (from Step 2), we get 0.16 * 12000 = 1920.
So, the number of invalid votes cast is 1920. Therefore, the correct option is 1920.
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