Percentage MCQ Quiz - Objective Question with Answer for Percentage - Download Free PDF

Given:

Population 4 years ago = 10,000

Annual growth rate for the first 2 years = 20%

Decrease rate in the third year = 10%

Decrease rate in the fourth year = 5%

Formula Used:

Population after n years = Initial Population × (1 + growth rate/100)^{number of years}

Calculation:

Population after first year = 10,000 × (1 + 20/100)

⇒ Population after first year = 10,000 × 1.2

⇒ Population after first year = 12,000

Population after second year = 12,000 × (1 + 20/100)

⇒ Population after second year = 12,000 × 1.2

⇒ Population after second year = 14,400

Population after third year = 14,400 × (1 - 10/100)

⇒ Population after third year = 14,400 × 0.9

⇒ Population after third year = 12,960

Population after fourth year = 12,960 × (1 - 5/100)

⇒ Population after fourth year = 12,960 × 0.95

⇒ Population after fourth year = 12,312

The current population of the city after four years is 12,312.

Shortcut Trick Population after fourth year = 10,000 × (1 + 20/100) × (1 + 20/100) × (1 - 10/100) × (1 - 5/100)

⇒ 10,000 × 1.2 × 1.2 × 0.9 × 0.95

⇒ 12,312

Given:

Poor product = 13%

Correct product = 5307

Calculation:

Let, the bad product = y

87% = 5307

1% = 5307 / 87 = 61

Bad product = 13 × 61 = 793

∴ The number of bad products = 793

Given:

Percentage of voters who restrained from voting = 25%

Percentage of invalid votes = 2%

Percentage of votes won by the candidate = 75%

Votes won by the candidate = 9261

Formula Used:

Total voters = Total votes cast / (1 - Percentage of voters who restrained from voting)

Valid votes = Total votes cast × (1 - Percentage of invalid votes)

Votes won by the candidate = Valid votes × Percentage of votes won by the candidate

Calculation:

Let the total number of voters be V.

Total votes cast = V × (1 - 0.25) = 0.75V

Valid votes = 0.75V × (1 - 0.02) = 0.75V × 0.98 = 0.735V

Votes won by the candidate = 0.735V × 0.75

⇒ 0.735V × 0.75 = 9261

⇒ 0.55125V = 9261

⇒ V = (9261)/(0.55125)

⇒ V = 16800

The total number of voters was 16800.

Concept used:

In such a question, we apply the compound per cent formula because the population is increasing compounded.

Formula used:

A = P(1 + r/100)ⁿ  where A = present population, P = population 2 year ago

R = per cent increase and n = time

60000 = P(1 + 25/100)²

P = 60000 × 4/5 × 4/5

P = 38400

Given:

Initial population of a town is 5500

Final population of a town is 6000

Male population increased by 5%

Female population increased by 10%

Calculation:

Let the number of males = x 

Number of females = (5500 - x)

According to the question,

⇒ Total Final population = Males + Females

⇒ 6000 = (x × 105) /100 + (5500 - x) × 110 /100

⇒ 6,00,000 = 105x  + ( 5500 × 110 - 110x )

⇒ 6,00,000 = 105x +  6,05,000 - 110x

⇒ 6,00,000 = 6,05,000 - 5x

⇒ -5x = - 5000 

⇒ x = 1000

∴ The number of men in the town is 1000.

Shortcut Trick 

Given:

Valid votes = 75% of total votes

Winning Candidate = 70% of Valid votes

He won by a majority of 3630 votes

Losing Candidate = 30% of Valid votes

Calculation:

Let 100x be the total number of votes polled

Valid votes = 75% of total votes

= 0.75 × 100x

= 75x

Majority of the Winning Candidate is 3630

Then, Difference between Winning and Losing Candidate = (70 % - 30 %) of valid votes

= 40% of the valid votes

Valid Votes = 75x

Then,

= 0.40 × 75x

= 30x

Hence, 30x is Majority of winning candidate

30x = 3630

x = 121

Total number of votes is 100x

= 100 × 121

= 12100

Answer is 12100.

GIVEN :

If the price of petrol has increased from Rs. 40 per litre to Rs. 60 per litre

CALCULATION :

Let the consumption be 100 litres.

When price is Rs. 40 per litres, then, the expenditure = 100 × 40

⇒ Rs. 4,000.

At Rs. 60 per litre, the 60 × consumption = 4000

Consumption = 4,000/60 = 66.67 litres.

∴ Required decreased % = 100 - 66.67 = 33.33%

Calculation:

Let the initial oranges with the fruit seller be x.

1st selling = 0.45x + 1

Remaining = x - (0.45x + 1) = 0.55x - 1

2nd selling = \(1\over 5\) × (0.55x - 1) = 0.11x - 0.2 + 2 = 0.11x + 1.8

Remaining after second selling = 0.55x - 1 - (0.11x + 1.8) = 0.55x - 0.11x - 1 - 1.8 = 0.44x - 2.8

3rd selling = 90% × (0.44x - 2.8)

Remaining after 3rd selling = 0.1 × (0.44x - 2.8) = 0.044x - 0.28

According to the question-

⇒ 0.044x - 0.28 = 5

⇒ 0.044x = 5.28

⇒ x = \(5.28\over 0.044\) = 120

∴ The number of oranges was 120. 

Alternate Method

At last, he sells 90% of the remaining oranges after selling the oranges to a second customer, then he has 10% of the remaining oranges.

10% of the remaining oranges after selling the oranges to the second customer = 5

So remaining oranges after selling the oranges to the second customer = 100% of the remaining oranges after selling the oranges to the second customer = 50 oranges

He gave 2 extra oranges to the second customer, so the remaining oranges = 50 + 2

He sells 20% of the remaining oranges to the second customer, so he has 80% of the remaining oranges = 52

100% of remaining oranges after selling the oranges to the first customer = (52/4) * 5 = 65 oranges

He gave 1 extra orange to the first customer, so the total oranges after selling 45% of the oranges = 65 + 1 = 66 oranges

(100% - 45% = 55%) of total oranges = 66

so

100% of oranges = (66/55) * 100 = 120 oranges

GIVEN :

The price of wheat is reduced by 4%.

ASSUMPTION :

Let the price of wheat be Rs.100/kg.

CALCULATION :

The price of 48 kg wheat  = 4800

As price is reduce by 4% it means that it became 96% of initial 100% hence,

After price decrease = 4800/96 = 50 kg

Hence, the required quantity of wheat = (50 – 48) = 2 kg more.

Given:

Initial population of a town is 5500

Final population of a town is 6000

Male population increased by 5%

Female population increased by 10%

Calculation:

Let the number of males = x 

Number of females = (5500 - x)

According to the question,

⇒ Total Final population = Males + Females

⇒ 6000 = (x × 105) /100 + (5500 - x) × 110 /100

⇒ 6,00,000 = 105x  + ( 5500 × 110 - 110x )

⇒ 6,00,000 = 105x +  6,05,000 - 110x

⇒ 6,00,000 = 6,05,000 - 5x

⇒ -5x = - 5000 

⇒ x = 1000

∴ The number of men in the town is 1000.

Shortcut Trick 

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:

Total number of students is 600000.

Calculation:

Out of 600000, 40% passed, the total number of passed students 600000 × 40/100 = 240000

Out of 600000, 40% were female, the total number of females = 240000 and males = 360000

The pass percentage among the males was 50%, total males passed= 360000/2 = 180000

So, female passed = (240000 - 180000) = 60000

So, female pass% = 60000/240000 × 100 = 25%

∴ The correct answer is 25%

Shortcut Trick 

Calculation:

The price of an umbrella decreased by 20%. [20% can be written as 1/5]

Let the initial price be = 5x.

After 20% decrease = 4x

Sales is increase by 40% [40% can be written as 2/5]

Let the initial sale be = 5x

After 40% increase = 7x

The ratio of the cost price and selling price = 25x:28x = 25:28

The net effect on revenue [net profit%] = \(\frac{{\left( {28 - 25} \right)}}{{25}} \times 100\)

⇒ 12% increase.

Hence, the correct answer is 12% increase.

Given:

There were two candidates in an election, 10% of voters did not vote and 48 votes were found invalid. The winning candidate got 53% of the total votes and won by 304 votes.

Concept used:

Percentage

Calculation:

Let the total number of voters be 100x

10% of voters did not vote 

Number of voters who vote = 100x - 10x = 90x

48 votes were found invalid

Valid votes = 90x - 48

Votes gained by the winning candidate = \(\frac{{53}}{{100}} \times 100x = 53x\)

Votes gained by the loosing candidate = 90x - 48 - 53x

⇒ 37x - 48

As per the question,

⇒ 53x - (37x - 48) = 304

⇒ 16x = 304 - 48

⇒ 16x = 256

⇒ x = 16

∴ Total number of voters = 100x = 1600

Alternate Method 

Let total number of votes be 100 units,

10% voters did not cast their vote

⇒ Votes polled = 90 units

The winning candidate got 53% of all the voters in the list and won by 304 votes,

⇒ Winning candidate got = 53 units votes

⇒ Other candidate got = 37 units votes

⇒ Difference in votes = 53 units votes - 37 units votes = 304 - 48 = 256 votes

⇒ 16 units = 256

∴ 100 units votes = 256/16 × 100 = 1600 votes

∴ Total number of voters = 1600.

Given:

Average is 280.

Formula used:

Average = sum of the observation/number of the observation     

Calculation:

Let the number be x

According to the question,

⇒ (x + 50% of x + 25% of x) / 3 = 280

⇒ (x + x/2 + x/4)/3 = 280

⇒ 7x/12 = 280

⇒ x =  480

∴ The number is 480.