Question

In an election between two candidates, 20 % of the voters didn't vote and 160 votes are declared invalid. The winner gets 39 % of the votes and declared win by 310 votes. Then find the number of voters in the voting list?

Answer 1

SOLUTION

CORRECT QUESTION

In an election between two candidates, 25 % of the voters didn't vote and 160 votes are declared invalid. The winner gets 39 % of the votes and declared win by 310 votes. Then find the number of voters in the voting list?

EVALUATION

Let the number of voters in the voting list = 100P

Now 25 % of the voters didn't vote

So the number of voters didn't vote

$= \displaystyle \sf{}100P \times \frac{25}{100}$

$= \sf{}25P$

So the number of voters vote

= 100P - 25P

= 75P

Now 160 votes are declared invalid

Total number of valid votes = 75P - 160

The winner gets 39 % of the votes

So the number of votes winner gets = 39P

So the number of votes winner gets

= 75P - 160 - 39P

= 36P - 160

By the given condition

$\sf{}39P - (36P - 160) = 310$

$\implies \sf{}39P - 36P + 160= 310$

$\implies \sf{}3P = 310 - 160$

$\implies \sf{}3P = 150$

$\implies \sf{}P = 50$

Hence the number of voters in the voting list

$\sf{} = 100 \times 50$

$= \sf{}5000$

NOTE ABOUT CORRECTION IN QUESTION

There information that 20 % of the voters didn't vote is not correct. If it was true then loosing candidate get more votes ( 41%- 160) than winning candidate (39%)

So the information is corrected to 25 % of the voters didn't vote

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Answer 2

Answer:

answer = 5000

Step-by-step explanation:

Let the number of voters in the voting list = 100P

Now 25 % of the voters didn't vote

So the number of voters didn't vote

So the number of voters vote

= 100P - 25P

= 75P

Now 160 votes are declared invalid

Total number of valid votes = 75P - 160

The winner gets 39 % of the votes

So the number of votes winner gets = 39P

So the number of votes winner gets

= 75P - 160 - 39P

= 36P - 160

By the given condition

Hence the number of voters in the voting list

=5000