In an election between two candidates, 80% of the registered voters cast their vote and 21% of the votes polled were found invalid. The winning candidate got 51% of the valid votes and won the election by a margin of 1817 votes. How many voters were registered?​

Correct option is A

Given:

Percentage of registered voters who voted = 80%

Percentage of invalid votes = 21%

Winning candidate secured = 51% of valid votes

Margin of victory = 1817 votes

Find the total number of registered voters

Solution:

Let the total number of registered voters be x

Votes polled = 80% of x = 0.8x

Invalid votes = 21%  of  0.8x = 0.168x

Valid votes = 0.8x - 0.168x = 0.632x

Winning candidate’s votes = 51% of valid votes = 0.51 × 0.632x

Losing candidate’s votes = 49%  of valid votes = 0.49 × 0.632x

Margin of victory = (0.51 - 0.49) × 0.632x = 0.02 × 0.632x

= 0.01264x

Given margin = 1817:

0.01264x = 1817

x = $$\frac{1817}{0.01264} \approx 143750$$​​

Number of registered voters = 143750

Alternate Solution(Exam - hall Trick):