In an election between two candidates, 75% of the voters cast their votes, out of which 2 % of the votes were declared invalid. A candidate got 9261 votes which were 75% of the total valid votes. Find the total number of voters enrolled in that election where each voter can cast only one vote.

Correct option is A

Given:

75% of the total voters cast their votes.

2% of the votes cast were invalid.

A candidate received 9261 votes, which is 75% of the valid votes.

Each voter can cast only one vote.

Solution:

Total votes cast = 75% of N

​$$\text{Total votes cast} = \frac{75}{100} \times N = 0.75N$$​​

Invalid votes = 2% of total votes cast

​$$\text{Invalid votes} = \frac{2}{100} \times 0.75N = 0.015N$$​​

Valid votes = Total votes cast - Invalid votes

​$$\text{Valid votes} = 0.75N - 0.015N = 0.735N$$​​

The candidate got 75% of valid votes

​$$9261 = \frac{75}{100} \times 0.735N$$​​

​$$9261 = 0.75 \times 0.735N$$​​

​$$N = \frac{9261}{0.55125}$$​​

N=16800

The total number of voters enrolled in the election is 16,800.