In an election between two candidates, P received 42% of the valid votes and Q won by 45,360 votes. 20% people did not cast their vote. If 10% of the votes cast were found invalid, what is the total number of votes registered in the poll booth?

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Accepted Answer

Let the total number of votes registered be N.

Given:
- 20% people did not cast their vote, so votes cast = 80% of N = 0.8N
- 10% of votes cast were invalid, so valid votes = 90% of votes cast = 0.9 × 0.8N = 0.72N

Candidate P received 42% of valid votes, so votes for P = 0.42 × 0.72N = 0.3024N

Candidate Q received the remaining valid votes = 0.58 × 0.72N = 0.4176N

Difference in votes = votes for Q - votes for P = 0.4176N - 0.3024N = 0.1152N

Given difference = 45,360

So, 0.1152N = 45,360
=> N = 45,360 / 0.1152
=> N = 393,750

Therefore, the total number of votes registered in the poll booth is 393,750.

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