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In an election, contested by two candidates, 5% of the voters did not cast their votes. The winning candidate won by 4900 votes, securing 51% of the total votes. How many votes were cast for the winning candidate?

In an election, contested by two candidates, 5% of the voters did not cast their votes. The winning candidate won by 4900 votes, securing 51% of the total votes. How many votes were cast for the winning candidate? Correct Answer 35,700

Given:

Winning candidate won by 4900 votes

Formula used:

Total votes = votes of the winner candidate + votes of the looser candidate

The difference of votes = votes of the winner candidate – votes of the looser candidate

Calculation:

Let total votes be x

Number of voters did not cast their votes = 5% of x = x/20

The winning candidate got votes = 51% of x = 51x/100

The number of votes losing candidate got = (x – x/20 – 51x/100) = 11x/25

Difference of votes = 51x/100 – 11x/25

⇒ 4900 = 7x/100

⇒ x = 70000

Votes cast for winning candidate = (51 × 70000)/100 = 35700

∴ The number of votes cast for winning candidate is 35700

Let the number of votes be 100%

The number of votes winning candidate got = 51%

The number of votes losing candidate got = (100% – 5% – 51%) = 44%

The difference in votes = 51% – 44% = 7%

Now, 7% = 4900

Then, 51% = 4900/7% × 51% = 35700

∴ The number of votes cast for winning candidate is 35700

Mistake Points Here the winning candidate got 51% of the total votes not of the valid votes.

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