Valid and Invalid Votes MCQ Quiz - Objective Question with Answer for Valid and Invalid Votes - Download Free PDF

Given:

80% of the voters cast their votes.

4% of the votes were declared invalid.

A candidate got 15,360 votes which were 80% of the valid votes.

Formula Used:

Total Votes = Total Voters × Percentage of Votes Cast

Valid Votes = Total Votes × Percentage of Valid Votes

Votes Received by Candidate = Valid Votes × Percentage of Votes Received

Calculation:

Let the total number of votes be x.

⇒ 80% of voters cast their votes:

⇒ Total Votes Cast = 0.80 × x

⇒ 4% of the votes were invalid:

⇒ Valid Votes = 0.96 × (0.80 × x)

⇒ Valid Votes = 0.96 × 0.80 × x

⇒ Valid Votes = 0.768 × x

A candidate got 15,360 votes which were 80% of the valid votes:

⇒ 15,360 = 0.80 × 0.768 × x

⇒ 15,360 = 0.6144 × x

Solving for x:

⇒ x = (15,360)/(0.6144)

⇒ x = 25,000

The total number of votes is 25,000.

Given:

P received 42% of the valid votes.

Q won by 45,360 votes.

20% people did not cast their vote.

10% of the votes cast were found invalid.

Formula Used:

Total votes = 100%

Votes cast = 80%

Invalid votes = 10% of 80% = 8%

Valid votes = 80% - 8% = 72%

Calculation:

Let total votes be V.

P's votes = 42% of 72% of V

Q's votes = 58% of 72% of V

Difference in votes = 58% of 72% of V - 42% of 72% of V = 45,360

⇒ 16% of 72% of V = 45,360

⇒ 0.16 × 0.72 × V = 45,360

⇒ V = 45,360 / (0.16 × 0.72)

⇒ V = 45,360 / 0.1152

⇒ V = 3,93,750

The total number of votes registered in the poll booth is 3,93,750.

Given:

X got 30% more votes than Y.

Z got 25% more votes than Y.

X overtook Z by 5000 votes.

71% of the voters voted.

Calculations:

Let the number of votes Y got be represented by y.

Thus, X got 1.30y votes and Z got 1.25y votes.

The total number of votes cast is 71% of the total number of voters (T).

Let the total number of voters be T.

The total number of votes cast is 0.71T.

Therefore, the total number of votes cast is the sum of votes received by X, Y, and Z:

⇒ 1.30y + y + 1.25y = 0.71T

⇒ 3.55y = 0.71T

Also, X overtook Z by 5000 votes:

⇒ 1.30y - 1.25y = 5000

⇒ 0.05y = 5000

⇒ y = 5000 / 0.05 = 100000

Substitute y = 100000 into 3.55y = 0.71T:

⇒ 3.55 × 100000 = 0.71T

⇒ 355000 = 0.71T

⇒ T = 355000 / 0.71 = 500000

The total number of voters in the voting list is 500,000.

Given:

One candidate gets 88% of the votes.

Majority of votes = 684 votes.

Formula Used:

Total votes = Majority votes / (Percentage difference / 100)

Calculation:

Let the total number of votes be V" id="MathJax-Element-39-Frame" role="presentation" style="position: relative;" tabindex="0">VV" id="MathJax-Element-580-Frame" role="presentation" style="position: relative;" tabindex="0">VV" id="MathJax-Element-63-Frame" role="presentation" style="position: relative;" tabindex="0">VV V V $V$ .

Candidate A gets 88% of the votes, so Candidate B gets (100% - 88%) = 12% of the votes.

The percentage difference between the two candidates = 88% - 12% = 76%

Majority votes = 684

Total votes = Majority votes / (Percentage difference / 100)

\(V = \frac{684}{76/100}\)

\(V = \frac{684 \times 100}{76}\)

\(V = \frac{68400}{76}\)

\(V = 900\)

The total number of votes polled is 900.

Given:

In a constituency:

45% of the total number of voters are males.

The rest of the voters are females (55%).

60% of the males are illiterate.

60% of the females are literate.

Formula used:

The percentage difference between illiterate females and literate males is given by:

\( \frac{\text{Illiterate females} - \text{Literate males}}{\text{Literate males}} \times 100 \)

Calculations:

Let the total number of voters be \( V \) (in arbitrary units).

The number of males = \( 0.45V \) and the number of females = \( 0.55V \).

The number of illiterate males = \( 60\% of males = 0.60 \times 0.45V = 0.27V \).

The number of illiterate females = \( 40\% of females = 0.40 \times 0.55V = 0.22V \).

The number of literate males = \( 40\% of males = 0.40 \times 0.45V = 0.18V \).

The number of literate females = \( 60\% of females = 0.60 \times 0.55V = 0.33V \).

Now, we are asked to find the percentage by which the number of illiterate females is more than the number of literate males:

\( \frac{\text{Illiterate females} - \text{Literate males}}{\text{Literate males}} \times 100 \)

\( \frac{0.22V - 0.18V}{0.18V} \times 100 = \frac{0.04V}{0.18V} \times 100 \)

\( \frac{0.04}{0.18} \times 100 \approx 22.22\% \)

Answer:

The number of illiterate females is approximately 22.22\% more than the number of literate males.

Given:

2% of voters did not cast their votes

Invalid votes = 500

The winner got 200 votes more than his opponent and he secured 43%

Calculation:

Let the total number of voters in the voting list be x

Total votes = (100 - 2)x/100 = 98x/100 = 0.98x

Total valid votes = 0.98x - 500

Number of votes loser got = 0.43x - 200

Total valid votes are:

⇒ 0.43x + 0.43x - 200 = 0.98x - 500

⇒ 0.86x - 200 = 0.98x - 500

⇒ 0.98x - 0.86x = 300

⇒ x = 2500

∴ The number of total casted votes = 2500 × (100 - 2)%

⇒ 2450

The number of total casted votes is 2450.

Given:

In an election between two candidates, the defeated candidate secured 42% of the valid votes polled and lost the election by 7,68,400 votes. 

82,560 votes were declared invalid and 20% of people did NOT cast their votes.

Calculation:

Percentage of total valid votes that winning candidate secured = (100 - 42) = 58%

% difference between the winning and defeated candidate = 58 - 42 = 16%

So, the total number of valid votes = 768400 ÷ 16% = 4802500

Total number of votes (both valid and invalid) = 4802500 + 82560 = 4885060

Total number of voters = 4885060 ÷ (100 - 20)% = 6106325

Number of people who didn't case vote = 6106325 × 20% = 1221265

Now, % = (82560/1221265) × 100% = 6.7602% ≈ 6.8%

∴ The invalid votes were 6.8% of the votes which people did NOT cast.

Given:

In an election between two candidates, 12% of voters did not cast their votes.

The winner by obtaining 68% of the total votes defeated his contestant by 2880 votes. 

Calculation:

Let total voters be 100a

So, total voters who casted their vote = 88a

Now,

Winner got 100a × 68%

⇒ 68a

So, losing candidate got 88a - 68a

⇒ 20a

According to the question,

68a - 20a = 2880

⇒ 48a = 2880

⇒ a = 60

So, number of voters who casted their votes = 60 × 88

⇒ 5280

∴ The total number of voters who cast their votes in the election was 5280.

Let the total number of votes be 100.

5% of votes polled were invalid = 5 votes

Raju got 30% of the total votes = 30 votes

Ravi got 32% of the total votes = 32 votes

Ashok got  = 100 - (30 + 32 + 5) = 33 votes

Raju got the least no. of votes and Ashok got the highest no. of votes.

Difference between votes got by Raju and Ashok = 3

⇒ 3 = 5136 ⇒ 1 = 1712 ⇒ 100 = 171200

∴  The total number of votes polled = 171200 votes.

Given:

Total votes cast = 90% × the total number of people on the electoral roll

Invalid votes = 15% ×  the votes cast at the election centre

Jeeta got 60% × valid votes

Jeeta got 91,800 valid votes

Calculation:

Let, the total number of people on the electoral roll = 100x

Total votes cast = 100x × 90% = 90x

Valid votes = 90x × 85%

According to the question:

⇒ 90x × 85% × 60% = 91800

⇒ 90x = (91800 × 100 × 10)/(85 × 6)

⇒ x = (180 × 100 × 10)/90

⇒ x = 2000

The total number of people on the electoral roll = 100x

⇒ 100 × 2000 = 200000 people

∴ The correct answer is 200000.

Given:

10% of the voters did not cast their vote and 10% of the polled vote were found invalid.

The winning candidate got 56% of the valid votes and won the election by a margin of 1,458 votes.

Concept Used:

The percentage is calculated based on 100 i.e. 100 is the base

40% means 40 out of 100

Calculation:

Let, the total enrolled voters be x

10% did not cast a vote means cast or polled vote = 9x/10

10% vote is invalid

That means valid vote = (90/100) × (9x/10)

⇒ 81x/100

The winning candidate got 56% of the polled vote means the looser got (100 – 56) = 44% vote

Winer candidate got total {(56/100) × (81x/100)} vote

And the looser candidate got {(44/100) × (81x/100)} vote

Accordingly,

{(56/100) × (81x/100)} - {(44/100) × (81x/100)} = 1458

⇒ (81x/100) × {(56 – 44)/100} = 1458

⇒ (81 × 12)x/10000 = 1458

⇒ x = (1458× 10000)/(81 × 12)

⇒ x = 15000

∴ Total 15000 voters enrolled in the voter list.

Shortcut Trick

Total voters = 1458 × (100/90) × (100/90) × 100\(56 - 44) = 15000

Given:

% voters who did not cast votes = 15%

Number of disqualified votes = 100

Winner candidate won by % of total votes = 45%

Winner candidate won by margin = 400 votes

Formula used:

Total votes cast  = Winner's votes + loser's votes - vote margin

Total votes cast = Total votes % - % votes who did not cast vote - disqualified votes.

Calculation:

​Let total voters be 100%x

Total votes cast = Total votes % - % votes who did not cast vote.

⇒ 100%x - 15%

⇒ 85%x

Votes got disqualified = 100

thus, Total votes cast = 85%x - 100

Winner got 45% of the total votes cast:

loser got = 45%x - 400

According to the question,

85% - 100 = 45%x + 45%x - 400

⇒ 300 = 90%x - 85%x

⇒ 300 = 5%x

⇒ x = 6000

∴ The total number of voters is 6000.

Given:

In a constituency, 85% of the total number of people on the electoral roll cast their votes during an election.

10% of the votes cast were declared invalid.

If there were 3,00,000 people on the electoral roll, and Dharam secured 1,37,700 valid votes.

Calculation:

The number of casted votes

⇒ 300000 × 85/100 =2,55,000

Number of valid votes,

⇒ 2,55,000 × 90 /100 = 229500

Percentage of votes Dharam secured

⇒ (137700 / 229500) × 100 = 60%

∴ The correct option is 4

Given:

There are 3 candidates in the election.

The third-place candidate got 20% of the total votes.

The difference between the votes of the winner and the first runner-up was 20% of the total votes.

The difference between the votes of the first runner-up and the second runner-up was 37,000 votes.

Formula used:

Percentage = (Part / Whole) × 100

Total = Part1 + Part2 + Part3

Solution:

Let 100x be the total number of votes.

Let the winners get votes and the 2nd runner-up get b votes.

The number of votes for the third-place candidate is 20% of total votes = 20x.

So the total number of votes winner and 2nd runner-up gets is

a + b + 20x = 100x

a + b = 80x ..........(1)

According to the question.

The difference in the votes between votes of the winner and the first runner-up was 20% of the total votes

So,

a - b = 20x......... (2)

Solving equation (1) & (2),

We get a = 50x and b = 30x

Now, the difference between the votes of the first runner-up and the second runner-up was 37,000

So, 30x - 20x = 37000

x = 3700

The number of votes for the winner is 50x = 50 × 3700 = 1,85,000

Therefore, the winner received 1,85,000 votes.

Shortcut Trick

Let's assume that total votes = 100 unit

So, person in 3^rd place got 20% which is = 20 unit remaining 80 unit

Difference of votes of 1st and 2nd is 20%, so winner must got 50 unit and 2^nd got 30 unit

According to the question, the difference of votes between 2^nd and 3^rd is 37000

So,(30 - 20) = 10 unit → 37,000

So, 50 unit → 37000/10 × 50 = 37000 × 5 = 185000

Given:

P got 35% more votes than Q

R got 15% more votes than Q.

P overtook R by 2,412 votes.

90% voters voted and no invalid or illegal votes were cast

Concept used:

Let the total votes of Q be 100x

P =  × 100x + 100x = 135x

R =  × 100x + 100x = 115x

Calculation:

135x - 115x = 2412

20x = 2412

x = 120.6

So, the vote obtained by Q = 100x = 100 × 120.6 = 12060

Vote obtained by P = 135x = 135 × 120.6 = 16281

Vote obtained by R = 115x = 115 × 120.6 = 13869

Total votes obtained by all of them = 12060 + 16281 + 13869 = 42210

Now, according to question, only 90% of the voters casted votes, therefore:

⇒ \(90 \over 100\) × y = 42210 ⇒ y = \(42210 \times 100 \over 90\) ⇒ y = 46900 (y = total votes)

Therefore, the number of voters in the voting list are 46900.