Percentage – mcqpedia.in

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[Concept: Fraction to %] If 16.66% of a number is 50, what will be 33.33% of that number?

Explanation: According to the fraction chart, 16.66% = 1/6. If x/6 = 50, then x = 300. Now, 33.33% (which is 1/3) of 300 is 100. (Short trick: Since 33.33% is double of 16.66%, the answer will be double of 50, which is 100).

[Concept: Fraction to %] If 8.33% of a number is 12, what is 25% of that number?

Explanation: According to the chart, 8.33% = 1/12. If x/12 = 12, then the original number x = 144. Now, 25% (which is 1/4) of 144 = 144/4 = 36.

[Concept: x% of y = y% of x] What is the value of 64% of 250?

Explanation: Using the concept x% of y = y% of x, we can write this as 250% of 64. 250% = 200% + 50% = (2 × 64) + (Half of 64) = 128 + 32 = 160. This makes calculation much faster.

[Concept: x% of y = y% of x] What is the value of 37.5% of 6400?

2400
3200
1800
2800

Explanation: From the fraction chart, 37.5% is equal to 3/8. Simply multiply: 3/8 × 6400 = 3 × 800 = 2400.

[Concept: What % is A of B] 120 is what percent of 150?

Explanation: The base is 150. Percentage = (120/150) × 100 = (4/5) × 100 = 80%.

[Concept: What % is A of B] 45 is what percent of 60?

75%
60%
80%
66.66%

Explanation: The base is 60. Percentage = (45/60) × 100 = (3/4) × 100 = 75%.

[Concept: What % Less/More] 90 is what percent less than 120?

25%
20%
33.33%
30%

Explanation: Difference = 120 – 90 = 30. The base is always the number after the word ‘than’. Base = 120. Percentage Less = (30/120) × 100 = 1/4 × 100 = 25%.

[Concept: What % Less/More] 150 is what percent more than 100?

50%
33.33%
60%
40%

Explanation: Difference = 150 – 100 = 50. The base is 100. Percentage More = (50/100) × 100 = 50%.

[Concept: Income & Tax] If the income tax increases by 18%, the net income decreases by 2%. What is the rate of income tax?

Explanation: Concept: Increase in Tax = Decrease in Net Income. Therefore, Tax × 18% = Net Income × 2%. Ratio (Tax / Net Income) = 2/18 = 1/9. Total Income = Tax + Net Income = 1 + 9 = 10. Rate of Tax = (Tax / Total Income) × 100 = (1/10) × 100 = 10%.

[Concept: Income & Tax] If the income tax increases by 21% and net income decreases by 4%, what was the initial tax rate?

Explanation: Formula: Tax × 21% = Net Income × 4%. Ratio (Tax : Net Income) = 4 : 21. Total Income = 4 + 21 = 25. Rate = (4 / 25) × 100 = 16%.

[Concept: Deviation Method] The ratio of expenditure on rice and dal in a family is 3:2. If the price of rice increases by 10% and dal by 20%, what is the overall percentage increase in expenditure?

Explanation: Using the Deviation method: Total percentage change = [(3 × 10%) + (2 × 20%)] / (3 + 2). Total = (30% + 40%) / 5 = 70% / 5 = 14% overall increase.

[Concept: Deviation Method] In a class, the ratio of boys to girls is 5:3. The number of boys increased by 12% and girls by 4%. What is the percentage increase in the total number of students?

Explanation: Using the Deviation method: Total percentage change = [(5 × 12%) + (3 × 4%)] / (5 + 3). Total = (60% + 12%) / 8 = 72% / 8 = 9% overall change.

[Concept: Population] The population of a village increases by 10% annually. If the current population is 5000, what will be the population after 2 years?

6050
6000
6100
6200

Explanation: Formula: P(1 + r/100)^t. Alternatively, use the multiplying factor: 10% increase = 11/10. Population = 5000 × (11/10) × (11/10) = 5000 × 1.21 = 6050.

[Concept: Population / Depreciation] The value of a machine depreciates by 20% every year. If its present value is 6400, what was its value 2 years ago?

10000
12000
8000
9600

Explanation: Let the value 2 years ago be P. According to the formula: P × (80/100) × (80/100) = 6400. So, P × (4/5) × (4/5) = 6400. P × 16/25 = 6400. P = (6400 × 25) / 16 = 400 × 25 = 10000.

[Concept: Same % Increase & Decrease] If the price of an article is first increased by 20% and then decreased by 20%, what is the net percentage change?

4% decrease
No change
4% increase
2% decrease

Explanation: Formula from the book: If a value is increased and decreased by the same percentage (x), there is always a net decrease of (x^2 / 100)%. Here x=20. Decrease = (20×20)/100 = 400/100 = 4% decrease.

[Concept: Same % Increase & Decrease] A man’s salary was reduced by 15% and then increased by 15%. What was the net effect on his salary?

2.25% decrease
2.25% increase
No change
3% decrease

Explanation: Formula: x^2 / 100% decrease. (15×15)/100 = 225/100 = 2.25%. It will always be a decrease.

[Concept: Successive Change] A number is first increased by 20% and then decreased by 10%. What is the net percentage change?

8% Increase
10% Increase
8% Decrease
12% Increase

Explanation: Formula: a + b + ab/100. Here a = +20, b = -10. Net change = 20 – 10 + (20 × -10)/100 = 10 – 2 = +8%. The positive sign indicates an 8% increase.

[Concept: Successive Change] The price of a shoe was reduced by 30% and then again reduced by 20%. What is the total equivalent discount given?

Explanation: Formula: a + b + ab/100. Here a = -30, b = -20. Net change = -30 – 20 + (-30 × -20)/100 = -50 + 6 = -44%. Thus, a total discount of 44% was given.

[Concept: Price & Consumption] The price of sugar increased by 25%. By what percent should a housewife reduce her consumption so that the expenditure remains the same?

20%
25%
16.66%
15%

Explanation: Formula from the book: If price increases by A%, consumption must be reduced by [A / (100+A)] × 100%. Here, [25 / (100+25)] × 100 = (25/125) × 100 = 1/5 × 100 = 20%.

[Concept: Price & Consumption] The price of petrol decreased by 20%. By what percent can a person increase his consumption for the same expenditure?

25%
20%
16.66%
30%

Explanation: Formula: If price decreases by A%, consumption can be increased by [A / (100-A)] × 100%. Here, [20 / (100-20)] × 100 = (20/80) × 100 = 1/4 × 100 = 25%.

[Concept: A more/less than B] A’s income is 20% more than B’s. By what percent is B’s income less than A’s?

16.66%
20%
25%
15%

Explanation: Formula: [A / (100+A)] × 100%. [20 / 120] × 100 = 1/6 × 100 = 16.66%. When the base changes, the percentage value changes.

[Concept: A more/less than B] If P is 25% less than Q, then Q is how much percent more than P?

33.33%
25%
20%
40%

Explanation: Formula: [A / (100-A)] × 100%. [25 / (100-25)] × 100 = (25/75) × 100 = 1/3 × 100 = 33.33% more.

[Concept: 2D Area Change] The length of a rectangle is increased by 20% and its breadth is increased by 10%. What will be the percentage change in its area?

32% Increase
30% Increase
28% Increase
33% Increase

Explanation: Book formula for Area: a + b + ab/100. Here, 20 + 10 + (20×10)/100 = 30 + 2 = 32% increase in Area.

[Concept: 2D Area Change] The radius of a circle is increased by 30%. What will be the percentage increase in its area?

Explanation: Area of a circle is proportional to r^2 (radius is multiplied twice). Formula: 2a + a^2/100. Here, 2(30) + (30^2)/100 = 60 + 900/100 = 60 + 9 = 69%.

[Concept: 3D Volume Change] Each side of a cube is increased by 10%. What will be the percentage increase in its volume?

33.1%
30%
31%
33.3%

Explanation: Book formula for volume: 3a + (3a^2)/100 + (a^3)/10000. Here a=10. Result: 3(10) + 3(100)/100 + 1000/10000 = 30 + 3 + 0.1 = 33.1%. (Alternatively, using multiplying factor: 1.1 × 1.1 × 1.1 = 1.331, which means a 33.1% increase).

[Concept: 3D Volume Change] The radius of a sphere is increased by 20%. What will be the percentage increase in its volume?

72.8%
60%
75%
80%

Explanation: Sphere Volume is proportional to r^3. The same cube formula applies: 3(20) + 3(400)/100 + 8000/10000 = 60 + 12 + 0.8 = 72.8% volume increase.

[Concept: Remaining Amount] A man gave 20% of his income to A, and 30% of the ‘remaining’ amount to B. Now he has 5600 left. What was his initial income?

10000
12000
8000
9000

Explanation: Book trick: Initial = Final × [100/(100-a)] × [100/(100-b)]. Here: Initial = 5600 × (100/80) × (100/70) = 5600 × (5/4) × (10/7) = 5600 × 50 / 28 = 200 × 50 = 10000.

[Concept: Remaining Amount] Ram spends 10% of his income and then spends 20% of the ‘remaining’ income. If he is left with 3600, what was his total income?

5000
4500
6000
7200

Explanation: Direct calculation: Income(x) × (90/100) × (80/100) = 3600. So, x × 0.72 = 3600. x = 3600 / 0.72 = 5000.

[Concept: Total Spending] A person spends 20% of his income on food, 30% on clothes, and 10% on rent. Now he is left with 8000. What was his total income? (Note: The word ‘remaining’ is not used here)

20000
16000
15000
25000

Explanation: If the word ‘remaining’ is not used, simply add the percentages. Total spent = 20% + 30% + 10% = 60%. Remaining = 40%. Given that 40% = 8000. So, 100% = (8000/40) × 100 = 20000.

[Concept: Total Spending] Anil spends 15% of his salary on education and 25% on bills. He is left with 12000. What is his total salary?

20000
18000
24000
25000

Explanation: Total spent = 15% + 25% = 40%. Remaining salary = 60%. If 60% = 12000, then 100% = 12000 × (100/60) = 200 × 100 = 20000.

[Concept: Venn Diagram] In an examination, 30% of students failed in Math, 40% failed in English, and 10% failed in both. What percentage of students passed in both subjects?

Explanation: Book formula: Fail in either = a + b – c. Here, Fail % = 30 + 40 – 10 = 60%. The students who failed in at least one subject are 60%. Therefore, Passed in both = 100% – 60% = 40%.

[Concept: Venn Diagram] In a village, 25% of people read newspaper A, 20% read newspaper B, and 5% read both. What percentage of people do not read any newspaper?

Explanation: People reading at least one newspaper (A U B) = n(A) + n(B) – n(A ∩ B) = 25 + 20 – 5 = 40%. So, people reading neither newspaper = 100% – 40% = 60%.

[Concept: Exam Passing Marks] A student needs 40% marks to pass. He gets 150 marks and fails by 50 marks. What are the total maximum marks of the exam?

Explanation: Marks required to pass = 150 (obtained) + 50 (failed margin) = 200 marks. According to the question, passing % = 40%. So, 40% = 200. Total (100%) = 200 × (100/40) = 500.

[Concept: Exam Passing Marks] A student needs 35% marks to pass. He gets 120 marks and fails by 20 marks. Find the maximum marks?

Explanation: Passing marks = 120 (obtained) + 20 (failed margin) = 140. Given that 35% = 140. Then 100% = 140 × (100/35) = 4 × 100 = 400.

[Concept: Price Reduction & Quantity] Due to a 20% reduction in the price of apples, a man can buy 5 kg more apples for Rs 400. What is the new (reduced) price per kg of apples?

Rs 16
Rs 20
Rs 25
Rs 12

Explanation: Book formula: New Price = (% Reduction × Total Amount) / Extra Quantity. New Price = (20% of 400) / 5 = (20 × 400 / 100) / 5 = 80 / 5 = Rs 16/kg.

[Concept: Price Reduction & Quantity] When the price of eggs drops by 10%, a man can buy 2 kg more eggs for Rs 360. What was the old (original) price per kg of eggs?

Rs 20
Rs 18
Rs 22
Rs 16

Explanation: Book formula for Old Price: (% Reduction × Total Amount) / [(100 – % Reduction) × Extra Quantity]. Old Price = (10 × 360) / (90 × 2) = 3600 / 180 = Rs 20/kg.

[Concept: Three Numbers Comparison] Two numbers are respectively 20% and 50% more than a third number. The first number is what percentage of the second number?

Explanation: Let the third number be 100. Then the first number is 120, and the second is 150. What percent is the first (120) of the second (150)? = (120 / 150) × 100 = 4/5 × 100 = 80%.

[Concept: Three Numbers Comparison] Two numbers are respectively 30% and 40% less than a third number. The first number is what percentage of the second number?

116.66%
114.28%
120%
110%

Explanation: Let the third number be 100. First number (30% less) = 70. Second number (40% less) = 60. The question asks: First (70) is what percent of Second (60)? = (70 / 60) × 100 = 7/6 × 100 = 116.66%.

[Concept: Election & Voting] In an election, the winning candidate got 55% of the total votes and won by 600 votes. What was the total number of votes cast? (Assume no invalid votes)

6000
5000
12000
6600

Explanation: Book formula: Total votes = (50 × Winning Margin) / (Winner’s % – 50). Total = (50 × 600) / (55 – 50) = 30000 / 5 = 6000. (Basic logic: Winner gets 55%, Loser gets 45%. Difference = 10%. If 10% = 600, then 100% = 6000).

[Concept: Election & Voting] An election was contested between two candidates. The winner got 60% of the votes and won by a margin of 1200 votes. How many total votes were cast?

6000
12000
8000
10000

Explanation: Difference in votes: Winner gets 60%, loser gets 40%. Winning margin = 20%. Given that 20% = 1200 votes. So, 100% (Total votes) = (1200 / 20) × 100 = 6000 votes.