Question

10% of the voters did not cast their vote in an election between two candidates. 10% of the votes polled were found invalid. The successful candidate got 54% of the valid votes and won by a majority of 1620 votes. The number of voters enrolled on the voters list was :
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Answer 1

Step-by-step explanation:

Given:

10% of the voters did not cast their vote in an election between two candidates. 10% of the votes polled were found invalid. The successful candidate got 54% of the valid votes and won by a majority of 1620 votes.

To Find:-

The number of voters enrolled on the voters list was

Solution:-

$\color{maroon} \rm \: Let \: the \: numer \:of \: votes \: enrolled \: be \: x$

No. of voters cast their vote=90% of x

No. of votes polled valid=90% of (90% of x)

$\rm \: Winner - 54\% \\ \rm \: Runner - 100 - 54 = 46\% \\ - - - - - - - - - - - - \\ \rm \: Difference = 54 - 16 = 8\%$

It is given that the winner won by the majority of 1620 votes. So, 8% of the votes enrolled (valid votes) is 1620 .So,

$\therefore \: \rm 8\% \: of \{90\%(90\% \: of \: x) \} = 1620 \\ \looparrowright \rm \: \: \frac{8}{100} \times \frac{90}{100} \times \frac{90}{100} \times x = 1620 \\ \looparrowright \rm \:x = \cancel \frac{16200 \times 100 \times 100 \times 100}{8 \times 90 \times 90} \\ \looparrowright \rm \: \color{olive}x = 25000$

[Number of votes enrolled is 25000]

ACQ,

Answer 2

Given :-

• No of voters who didn't cast vote = 10%
• No of invalid voters in election = 10%
• The successful candidate got vote = 54%
• The successful candidate won by = 1620 V

To Find :-

• The no of voters enroll in voters list = ?

Solution :-

To calculate the no of voters who voted in the election at first we have to set up equation as per the given clue in the question. The clues are 10% of the voters did not cast their vote in an election between two candidates. 10% of the votes polled were found invalid. The successful candidate got 54% of the valid votes and won by a majority of 1620 votes. Let assume the total number of votes who voted in the election be x .

Calculation begins :-

⇒ No of valid votes = 100 - 20 = 80%

⇒ No of total votes = x * 80/100 = 80x/100

⇒ winners candidate got votes = 54% of 80x/100

⇒ Losser candidate got votes = 100 - 54 = 46%

Let's set up equation here :-

⇒ Winner votes - Losser votes = 1620

⇒ 54/100 * 80x/100 - 46/100 * 80x/100 = 1620

⇒ 54 * 4x/5 * 100 - 46 * 4x/5 * 100 = 1620

⇒ 216x/500 - 176x/500 = 1620

⇒ 216x - 176x/500 = 1620

⇒ 40x = 1620 × 500

⇒ 4x = 1620 × 50

⇒ 4x = 81000

⇒ x = 20250

Hence,

⇒ Total votes were pulled in election = 20250