IAS 2022 — CSAT Maths

Correct Option

Let the total number of voters in the voters list be $T$T.

According to the problem statement:

• 80% of voters cast their vote.
• Total votes cast = $80\%$80% of $T = \frac{80}{100} \times T = 0.8T$T=10080​×T=0.8T.
• Candidate X received 56% of the votes cast.
• Candidate Y received $(100\% - 56\%) = 44\%$(100%−56%)=44% of the votes cast.
• The winning margin for X was 1440 votes.

The difference in votes between Candidate X and Candidate Y equals the winning margin:

Votes for X - Votes for Y = 1440

$56\%$56% of $(0.8T) - 44\%$(0.8T)−44% of $(0.8T) = 1440$(0.8T)=1440

$(56\% - 44\%)$(56%−44%) of $(0.8T) = 1440$(0.8T)=1440

$12\%$12% of $(0.8T) = 1440$(0.8T)=1440

This can be written as:

$$1440 = \frac{12}{100} \times \frac{8}{10}T$$1440=10012​×108​T

To solve for $T$T:

$T = \frac{1440 \times 100 \times 10}{12 \times 8}$T=12×81440×100×10​

$T = \frac{1440000}{96}$T=961440000​

$$T = 15000$$T=15000

Therefore, the total number of voters in the voters list is 15000.

Incorrect Options

Options 2 (12000), 3 (9600), and 4 (5000) are incorrect because they do not satisfy the conditions derived from the problem statement regarding the percentage of votes cast, the vote distribution between candidates X and Y, and the specified winning margin of 1440 votes.