Question 1

A merchant bought goods for ₹8,000. He wants to make a profit of 25%. At what price should he sell the goods?

Accepted Answer

Step 1: Cost price = ₹8,000. Required profit percentage = 25%. Step 2: Profit = 25% of 8,000 = (25/100) × 8,000 = ₹2,000. Step 3: Selling price = Cost price + Profit = 8,000 + 2,000 = ₹10,000.

Question 2

A shopkeeper marks his goods 40% above the cost price. If he gives a discount of 10% on the marked price, what is his profit percentage?

Accepted Answer

Step 1: Let cost price = 100. Marked price = 100 + 40% of 100 = 140. Step 2: Discount = 10% of 140 = 14. Selling price = 140 - 14 = 126. Step 3: Profit = 126 - 100 = 26. Profit percentage = (26/100) × 100 = 26%.

Question 3

In an examination, 65% of students passed in English and 75% passed in Mathematics. If 15% failed in both subjects, what percentage of students passed in both subjects?

Accepted Answer

Step 1: Students who failed in English = 100 - 65 = 35%. Students who failed in Mathematics = 100 - 75 = 25%. Step 2: Using the principle: Failed in at least one subject = Failed in English + Failed in Math - Failed in both = 35 + 25 - 15 = 45%. Step 3: Passed in both = 100 - 45 = 55%.

Question 4

The price of a commodity increased by 20% in the first year and decreased by 25% in the second year. What is the net change in price over two years?

Accepted Answer

Step 1: Let original price = 100. After 20% increase: Price = 100 + 20 = 120. Step 2: After 25% decrease on 120: Price = 120 - (25% of 120) = 120 - 30 = 90. Step 3: Net change = 90 - 100 = -10. Net change percentage = (-10/100) × 100 = -10% (decrease).

Question 5

A student scored 45% marks in an examination and failed by 36 marks. If passing marks are 55%, how many total marks were there in the examination?

Accepted Answer

Step 1: Let total marks = x. Marks scored = 45% of x = 0.45x. Passing marks = 55% of x = 0.55x. Step 2: The student failed by 36 marks, so: 0.55x - 0.45x = 36. Step 3: 0.10x = 36, therefore x = 360.

Question 6

A town's population was 50,000 in 2020. It increased by 10% in 2021 and by 20% in 2022. What was the population in 2022?

Accepted Answer

Step 1: Population in 2020 = 50,000. Population in 2021 = 50,000 + 10% of 50,000 = 50,000 + 5,000 = 55,000. Step 2: Population in 2022 = 55,000 + 20% of 55,000 = 55,000 + 11,000 = 66,000.

Question 7

A shopkeeper marks goods at 60% above the cost price. He then offers a discount of 25% on the marked price. If the cost price of an item is ₹800, what is his profit percentage?

Accepted Answer

Step 1: Calculate Marked Price (MP). MP = Cost Price + 60% of CP = 800 + (60/100) × 800 = 800 + 480 = ₹1,280. Step 2: Calculate Selling Price (SP) after 25% discount. Discount = 25% of MP = (25/100) × 1,280 = ₹320. SP = MP − Discount = 1,280 − 320 = ₹960. Step 3: Calculate Profit Percentage. Profit = SP − CP = 960 − 800 = ₹160. Profit % = (Profit/CP) × 100 = (160/800) × 100 = 20%. Therefore, the profit percentage is 20%.

Question 8

A shopkeeper marks up goods by 40% above cost price. He then offers a discount of 20% on the marked price. If the cost price of an item is ₹500, what is his profit percentage?

Accepted Answer

Step 1: Cost Price (CP) = ₹500. Marked Price (MP) = 500 + 40% of 500 = 500 + 200 = ₹700. Step 2: Discount = 20% of 700 = 140. Selling Price (SP) = 700 - 140 = ₹560. Step 3: Profit = 560 - 500 = ₹60. Profit % = (60/500) × 100 = 12%.

Question 9

In a school, 60% of students are boys. If 25% of boys and 40% of girls passed an exam, what percentage of the total students passed?

Accepted Answer

Step 1: Assume total students = 100. Boys = 60, Girls = 40. Step 2: Boys who passed = 25% of 60 = 15. Girls who passed = 40% of 40 = 16. Step 3: Total passed = 15 + 16 = 31. Percentage = (31/100) × 100 = 31%.

Question 10

A person's salary increases by 20% in the first year and then decreases by 10% in the second year. If his final salary is ₹10,800, what was his original salary?

Accepted Answer

Step 1: Let original salary = x. After 20% increase: x × 1.20 = 1.20x. Step 2: After 10% decrease: 1.20x × 0.90 = 1.08x. Step 3: 1.08x = 10,800. x = 10,800 ÷ 1.08 = ₹10,000.

Question 11

A merchant buys goods at ₹80 per unit. He sells 70% of the stock at 25% profit and the remaining 30% at 10% loss. What is his overall profit or loss percentage?

Accepted Answer

Step 1: Assume 100 units at ₹80 each. Total CP = ₹8,000. Step 2: 70 units sold at 25% profit: SP = 70 × 80 × 1.25 = ₹7,000. Step 3: 30 units sold at 10% loss: SP = 30 × 80 × 0.90 = ₹2,160. Step 4: Total SP = 7,000 + 2,160 = ₹9,160. Step 5: Profit = 9,160 - 8,000 = ₹1,160. Profit % = (1,160/8,000) × 100 = 14.5%.

Question 12

The price of petrol increases by 30%. By what percentage should a consumer reduce his consumption to keep his expenditure unchanged?

Accepted Answer

Step 1: Let original price = P, original consumption = C, original expenditure = P × C. Step 2: New price = 1.30P. Let new consumption = C'. Step 3: For unchanged expenditure: 1.30P × C' = P × C. C' = C/1.30 = C × (10/13). Step 4: Reduction = C - (10C/13) = 3C/13. Reduction % = (3C/13)/C × 100 = (3/13) × 100 ≈ 23.08%, which rounds to approximately 23.08% or exactly 300/13 %.

Question 13

A shopkeeper marks up goods by 60% above cost price. He then offers a discount of 25% on the marked price. If the cost price of an item is ₹800, what is his profit percentage?

Accepted Answer

Step 1: Cost Price (CP) = ₹800. Marked Price (MP) = 800 + 60% of 800 = 800 + 480 = ₹1280. Step 2: Discount = 25% of 1280 = 320. Selling Price (SP) = 1280 - 320 = ₹960. Step 3: Profit = 960 - 800 = ₹160. Step 4: Profit % = (160/800) × 100 = 20%.

Question 14

A person's salary increases by 20% in year 1 and by 25% in year 2. In year 3, the salary decreases by 10%. If the final salary after 3 years is ₹54,000, what was the original salary?

Accepted Answer

Step 1: Let original salary = x. After year 1: x × 1.20. After year 2: x × 1.20 × 1.25 = x × 1.50. After year 3: x × 1.50 × 0.90 = x × 1.35 = 54,000. Step 2: x = 54,000 ÷ 1.35 = 40,000. Verification: 40,000 × 1.20 = 48,000; 48,000 × 1.25 = 60,000; 60,000 × 0.90 = 54,000. ✓

Question 15

In an election, candidate A received 45% of votes, candidate B received 35% of votes, and the remaining votes were invalid. If candidate A won by 2,000 votes over candidate B, how many total votes were cast?

Accepted Answer

Step 1: Let total votes = x. Candidate A = 0.45x, Candidate B = 0.35x. Step 2: Difference = 0.45x - 0.35x = 0.10x = 2,000. Step 3: x = 2,000 ÷ 0.10 = 20,000. Verification: A = 9,000 votes, B = 7,000 votes, difference = 2,000. ✓

Question 16

A student scored 72% in English and 68% in Mathematics. If the maximum marks in each subject is 100, what is the average percentage scored by the student?

Accepted Answer

Step 1: Marks in English = 72% of 100 = 72. Step 2: Marks in Mathematics = 68% of 100 = 68. Step 3: Total marks obtained = 72 + 68 = 140. Step 4: Total maximum marks = 100 + 100 = 200. Step 5: Average percentage = (140/200) × 100 = 70%.

Question 17

A student scored 45% marks in an examination and failed by 36 marks. If the passing percentage is 55%, what are the total marks of the examination?

Accepted Answer

Step 1: Let total marks = x. Student scored 45% of x. Passing marks = 55% of x. Step 2: Difference between passing marks and obtained marks = 55% of x - 45% of x = 10% of x = 36. Step 3: 10% of x = 36, so x = 36 × 10 = 360.

Question 18

A shopkeeper marks his goods at 40% above the cost price. If he gives a discount of 10% on the marked price, what is his profit percentage?

Accepted Answer

Step 1: Let cost price = 100. Marked price = 100 + 40% of 100 = 140. Step 2: Discount = 10% of 140 = 14. Selling price = 140 - 14 = 126. Step 3: Profit = 126 - 100 = 26. Profit percentage = (26/100) × 100 = 26%.

Question 19

A mobile phone costs ₹8000. During a sale, it is offered at 15% discount. What is the sale price?

Accepted Answer

Step 1: Original price = ₹8000. Step 2: Discount = 15% of 8000 = 0.15 × 8000 = ₹1200. Step 3: Sale price = 8000 - 1200 = ₹6800.

Question 20

In an examination, 35% of the students failed in Mathematics and 28% failed in English. If 10% failed in both subjects, what percentage of students passed in both subjects?

Accepted Answer

Step 1: Students who failed in at least one subject = Failed in Math + Failed in English - Failed in both = 35% + 28% - 10% = 53%. Step 2: Students who passed in both subjects = 100% - 53% = 47%.

Question 21

The price of a book increased by 25%. If the new price is ₹500, what was the original price?

Accepted Answer

Step 1: Let original price = x. Step 2: New price = x + 25% of x = 1.25x. Step 3: 1.25x = 500. Step 4: x = 500/1.25 = 400. Therefore, original price was ₹400.

Question 22

A factory produces 1200 units in January. In February, production increased by 20%. How many units were produced in February?

Accepted Answer

Step 1: Production in January = 1200 units. Step 2: Increase = 20% of 1200 = 0.20 × 1200 = 240 units. Step 3: Production in February = 1200 + 240 = 1440 units.

Question 23

The price of petrol increased by 20% last month and then decreased by 20% this month. If the original price was ₹80 per litre, what is the current price?

Accepted Answer

Step 1: Price after 20% increase = 80 + 20% of 80 = 80 + 16 = ₹96. Step 2: Price after 20% decrease = 96 - 20% of 96 = 96 - 19.2 = ₹76.8.

Question 24

A shopkeeper buys a shirt for ₹400. He marks it up by 50% and then gives a discount of 20% on the marked price. What is his profit percentage?

Accepted Answer

Step 1: Cost Price (CP) = ₹400. Step 2: Marked Price (MP) = 400 + 50% of 400 = 400 + 200 = ₹600. Step 3: Discount = 20% of 600 = 120. Step 4: Selling Price (SP) = 600 - 120 = ₹480. Step 5: Profit = 480 - 400 = ₹80. Step 6: Profit % = (80/400) × 100 = 20%.

Question 25

A retailer buys goods at ₹80 per unit. He marks them up by 50% and offers a discount of 20% during a sale. Additionally, he gives a loyalty bonus of 5% off the discounted price to regular customers. What is the final selling price for a regular customer, and what is his profit percentage?

Accepted Answer

Step 1: Cost Price (CP) = ₹80. Step 2: Marked Price (MP) = 80 + 50% of 80 = 80 × 1.50 = ₹120. Step 3: Price after 20% discount = 120 × 0.80 = ₹96. Step 4: Final price after 5% loyalty bonus = 96 × 0.95 = ₹91.20. Step 5: Profit = Selling Price − Cost Price = 91.20 − 80 = ₹11.20. Step 6: Profit % = (11.20 / 80) × 100 = 14%. Therefore, the final selling price is ₹91.20 and profit percentage is 14%.

Question 26

A shopkeeper marks up goods by 40% above cost price. He then offers a discount of 20% on the marked price. If the cost price of an item is ₹500, what is his profit percentage?

Accepted Answer

Step 1: Marked Price = Cost Price + 40% of Cost Price = 500 + 0.40(500) = 500 + 200 = ₹700. Step 2: Selling Price = Marked Price − 20% of Marked Price = 700 − 0.20(700) = 700 − 140 = ₹560. Step 3: Profit = Selling Price − Cost Price = 560 − 500 = ₹60. Step 4: Profit % = (Profit / Cost Price) × 100 = (60 / 500) × 100 = 12%. Therefore, the profit percentage is 12%.

Question 27

In a school, 60% of students are boys. If 25% of boys and 40% of girls participate in sports, what percentage of the total student population participates in sports?

Accepted Answer

Step 1: Let total students = 100. Boys = 60% of 100 = 60. Girls = 40% of 100 = 40. Step 2: Boys in sports = 25% of 60 = 0.25 × 60 = 15. Step 3: Girls in sports = 40% of 40 = 0.40 × 40 = 16. Step 4: Total students in sports = 15 + 16 = 31. Step 5: Percentage = (31/100) × 100 = 31%. Therefore, the answer is 31%.

Question 28

A product's price is increased by 20%, then decreased by 25%, and finally increased by 10%. If the final price is ₹990, what was the original price?

Accepted Answer

Step 1: Let original price = P. Step 2: After 20% increase: Price = 1.20P. Step 3: After 25% decrease: Price = 1.20P × 0.75 = 0.90P. Step 4: After 10% increase: Price = 0.90P × 1.10 = 0.99P. Step 5: Given final price = ₹990, so 0.99P = 990. Step 6: P = 990 / 0.99 = ₹1,000. Therefore, the original price was ₹1,000.

Question 29

In a college, 60% of students are boys and 40% are girls. If 25% of boys and 10% of girls participate in sports, what percentage of the total student population participates in sports?

Accepted Answer

Step 1: Let total students = 100 (for easy calculation). Boys = 60% of 100 = 60. Girls = 40% of 100 = 40. Step 2: Boys in sports = 25% of 60 = 0.25 × 60 = 15. Step 3: Girls in sports = 10% of 40 = 0.10 × 40 = 4. Step 4: Total students in sports = 15 + 4 = 19. Step 5: Percentage of total = (19 / 100) × 100 = 19%. Therefore, 19% of the total student population participates in sports.

Question 30

A product's price was reduced by 30%, and then the new price was increased by 30%. If the final price is ₹273, what was the original price?

Accepted Answer

Step 1: Let original price = x. After 30% reduction: Price = x × 0.70 = 0.7x. Step 2: After 30% increase on the reduced price: Price = 0.7x × 1.30 = 0.91x. Step 3: Given final price = ₹273. So, 0.91x = 273. Step 4: x = 273 ÷ 0.91 = ₹300. Therefore, the original price was ₹300.

Question 31

A person's salary increased by 20% in the first year. In the second year, it decreased by 10%. If his final salary is ₹10,800, what was his original salary?

Accepted Answer

Step 1: Let original salary = x. After 20% increase: Salary = x × 1.20 = 1.2x. Step 2: After 10% decrease in second year: Salary = 1.2x × 0.90 = 1.08x. Step 3: Given that final salary = ₹10,800. So, 1.08x = 10,800. Step 4: x = 10,800 ÷ 1.08 = ₹10,000. Therefore, the original salary was ₹10,000.

Question 32

A person's salary is increased by 15% in the first year and then decreased by 10% in the second year. If his final salary is ₹10,350, what was his original salary?

Accepted Answer

Step 1: Let original salary = x. Step 2: After 15% increase: Salary = x + 0.15x = 1.15x. Step 3: After 10% decrease on the new salary: Final Salary = 1.15x − 0.10(1.15x) = 1.15x(1 − 0.10) = 1.15x × 0.90 = 1.035x. Step 4: Given that final salary = ₹10,350, so 1.035x = 10,350. Step 5: x = 10,350 / 1.035 = ₹10,000. Therefore, the original salary was ₹10,000.

Question 33

A shopkeeper marks up the cost price of an item by 40%. During a sale, he offers a discount of 25% on the marked price. If the cost price is ₹800, what is his profit percentage?

Accepted Answer

Step 1: Cost Price (CP) = ₹800. Marked Price (MP) = 800 + 40% of 800 = 800 × 1.4 = ₹1120. Step 2: Discount = 25% of 1120 = 0.25 × 1120 = ₹280. Selling Price (SP) = 1120 − 280 = ₹840. Step 3: Profit = SP − CP = 840 − 800 = ₹40. Step 4: Profit % = (40/800) × 100 = 5%. Therefore, the answer is 5%.

Question 34

In a college, 40% of students are in Science, 35% are in Commerce, and the remaining are in Arts. If 20% of Science students and 30% of Commerce students pass an entrance exam, what percentage of the total student body passed the exam?

Accepted Answer

Step 1: Let total students = 100. Science students = 40, Commerce students = 35, Arts students = 25. Step 2: Science students who passed = 20% of 40 = 8. Step 3: Commerce students who passed = 30% of 35 = 10.5. Step 4: Total passed = 8 + 10.5 = 18.5. Step 5: Percentage of total = (18.5 ÷ 100) × 100 = 18.5%.

Question 35

A book's price is increased by 20%, then a discount of 15% is offered on the new price. Later, an additional 10% discount is given on the already-discounted price. If the final price is ₹918, what was the original price?

Accepted Answer

Step 1: Let original price = P. After 20% increase: P₁ = P × 1.20. Step 2: After first discount of 15%: P₂ = P₁ × 0.85 = P × 1.20 × 0.85 = P × 1.02. Step 3: After second discount of 10%: P₃ = P₂ × 0.90 = P × 1.02 × 0.90 = P × 0.918. Step 4: Given P₃ = ₹918, so P × 0.918 = 918. Step 5: P = 918 ÷ 0.918 = ₹1,000.

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