In an election between P, R, and S, of the total votes polled are invalid. Votes polled in favor of R and S are half of the total votes polled, and they get equal votes. Due to a fault in the machine, half of the votes of S and half of the invalid votes are counted additionally in favor of R. What is the overall percentage of votes secured by R due to the fault?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 42.5%.
Let the total votes polled = 100x
Invalid votes = 1/10 of 100x = 10x
Valid votes = 100x - 10x = 90x
Votes polled in favor of R and S together are half of the total votes = (1/2) × 100x = 50x
Since R and S get equal votes:
Votes for R = Votes for S = (1/4) × 100x = 25x
Due to a fault in the machine:
Half of S's votes = (1/2) × (1/4) × 100x = 12.5x are added to R.
Half of the invalid votes = (1/2) × (1/10) × 100x = 5x are also added to R.
Total votes for R after the fault:
Votes originally for R + Half of S's votes + Half of invalid votes.
= 25x + 12.5x + 5x
= 42.5x
Required percentage = 42.5x/100x × 100 = 42.5%