Question 1

A student scored 360 marks out of 500 in an examination. What percentage of marks did the student score?

Accepted Answer

Step 1: Use the formula: Percentage = (Marks obtained / Total marks) × 100. Step 2: Percentage = (360 / 500) × 100 = 72%. Therefore, the student scored 72%.

Question 2

A shopkeeper bought a shirt for ₹400. He marked it up by 50% and then gave 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 = 0.20 × 600 = ₹120. Step 4: Selling Price (SP) = 600 - 120 = ₹480. Step 5: Profit = SP - CP = 480 - 400 = ₹80. Step 6: Profit % = (80/400) × 100 = 20%. Therefore, the answer is 20%.

Question 3

A student scored 75% marks in an exam. If the total marks were 320, how many marks did the student score?

Accepted Answer

Step 1: Total marks = 320. Step 2: Percentage scored = 75%. Step 3: Marks scored = 75% of 320 = (75/100) × 320 = 0.75 × 320 = 240. Therefore, the student scored 240 marks.

Question 4

In an exam, 65% of students passed in Mathematics and 75% passed in English. If 55% passed in both subjects, what percentage of students failed in both subjects?

Accepted Answer

Step 1: Let total students = 100. Step 2: Students who passed Math = 65. Students who passed English = 75. Students who passed both = 55. Step 3: Using set theory: Students who passed at least one subject = (Passed Math) + (Passed English) - (Passed both) = 65 + 75 - 55 = 85. Step 4: Students who failed both subjects = 100 - 85 = 15. Therefore, 15% of students failed in both subjects.

Question 5

In an exam, 60% of students passed. If 240 students passed, how many students appeared for the exam in total?

Accepted Answer

Step 1: Let total students = x. Step 2: 60% of x = 240. Step 3: (60/100) × x = 240. Step 4: 0.6x = 240. Step 5: x = 240 ÷ 0.6 = 400. Therefore, total students = 400.

Question 6

A shopkeeper buys a shirt for ₹400. He wants to make a profit of 25% on the cost price. At what price should he sell the shirt?

Accepted Answer

Step 1: Cost Price (CP) = ₹400. Step 2: Profit % = 25%. Step 3: Profit = 25% of 400 = (25/100) × 400 = ₹100. Step 4: Selling Price (SP) = CP + Profit = 400 + 100 = ₹500. Therefore, the answer is ₹500.

Question 7

A student scored 45% marks in an exam and failed by 36 marks. If passing marks are 60%, how many total marks were there in the exam?

Accepted Answer

Step 1: Let total marks = x. Step 2: Student scored 45% of x = 0.45x. Step 3: Passing marks = 60% of x = 0.60x. Step 4: Difference between passing marks and student's marks = 0.60x - 0.45x = 36. Step 5: 0.15x = 36. Step 6: x = 36/0.15 = 240. Therefore, total marks = 240.

Question 8

The price of petrol increased by 25%. By what percentage should a consumer reduce consumption to keep the expenditure the same?

Accepted Answer

Step 1: Let original price = P and original consumption = C. Original expenditure = P × C. Step 2: New price = P + 25% of P = 1.25P. Step 3: Let new consumption = C'. For expenditure to remain same: 1.25P × C' = P × C. Step 4: C' = (P × C)/(1.25P) = C/1.25 = 0.8C. Step 5: Reduction in consumption = C - 0.8C = 0.2C. Step 6: Percentage reduction = (0.2C/C) × 100 = 20%. Therefore, consumption should be reduced by 20%.

Question 9

A company's revenue increased by 20% in the first year and then decreased by 10% in the second year. If the initial revenue was ₹50,000, what is the revenue after two years?

Accepted Answer

Step 1: Initial revenue = ₹50,000. Step 2: After 20% increase in year 1: Revenue = 50,000 × (1 + 20/100) = 50,000 × 1.2 = ₹60,000. Step 3: After 10% decrease in year 2: Revenue = 60,000 × (1 - 10/100) = 60,000 × 0.9 = ₹54,000. Therefore, final revenue = ₹54,000.

Question 10

A mobile phone was sold for ₹18,000 at a loss of 10%. What was the cost price of the mobile phone?

Accepted Answer

Step 1: Selling Price (SP) = ₹18,000. Step 2: Loss = 10%. Step 3: If loss is 10%, then SP = 90% of CP. Step 4: 90% of CP = 18,000. Step 5: CP = 18,000 ÷ 0.9 = 20,000. Therefore, cost price = ₹20,000.

Question 11

In an examination, 35% of students failed in Mathematics, 25% failed in English, and 10% failed in both subjects. What percentage of students passed in both subjects?

Accepted Answer

Step 1: Let total students = 100. Students who failed in Math = 35. Students who failed in English = 25. Students who failed in both = 10. Step 2: Using set theory: Failed in at least one subject = 35 + 25 - 10 = 50. Step 3: Passed in both subjects = 100 - 50 = 50%.

Question 12

A company's revenue increased from ₹50 lakhs to ₹65 lakhs. What is the percentage increase in revenue?

Accepted Answer

Step 1: Increase in revenue = 65 - 50 = ₹15 lakhs. Step 2: Percentage increase = (Increase / Original) × 100 = (15 / 50) × 100 = 30%.

Question 13

A shopkeeper marks his goods 40% above the cost price. If he gives a discount of 20% 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 = 20% of 140 = 28. Selling price = 140 - 28 = 112. Step 3: Profit = 112 - 100 = 12. Profit percentage = (12/100) × 100 = 12%.

Question 14

In an election, candidate A received 55% of the votes and candidate B received the remaining votes. If the total number of votes cast was 8000, by how many votes did A win?

Accepted Answer

Step 1: Votes received by A = 55% of 8000 = 0.55 × 8000 = 4400. Step 2: Votes received by B = 8000 - 4400 = 3600. Step 3: Winning margin = 4400 - 3600 = 800 votes.

Question 15

A student scored 72% in English and 88% in Mathematics. If English has a weightage of 40% and Mathematics has a weightage of 60%, what is the student's overall percentage?

Accepted Answer

Step 1: Weighted score = (72 × 40%) + (88 × 60%). Step 2: = (72 × 0.40) + (88 × 0.60) = 28.8 + 52.8 = 81.6%.

Question 16

A person's salary is increased by 20% in the first year and then decreased by 10% in the second year. If his final salary is ₹21,600, what was his original salary?

Accepted Answer

Step 1: Let original salary = x. After 20% increase: x × 1.20 = 1.2x. Step 2: After 10% decrease on new salary: 1.2x × 0.90 = 1.08x. Step 3: Given 1.08x = 21,600. Therefore, x = 21,600 ÷ 1.08 = ₹20,000.

Question 17

A product's price was reduced by 30%. If the reduced price is ₹420, what was the original price?

Accepted Answer

Step 1: Let original price = x. After 30% reduction: price = x - 0.30x = 0.70x. Step 2: 0.70x = 420. Step 3: x = 420 / 0.70 = 600. Original price = ₹600.

Question 18

A shopkeeper marks his goods 40% above the cost price. He then offers a discount of 20% on the marked price. If the cost price of an article 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 19

A person's salary increases by 20% in the first year and then decreases by 20% in the second year. If his original salary was ₹50,000, what is his salary after two years?

Accepted Answer

Step 1: After first year increase of 20%: Salary = 50,000 × 1.20 = ₹60,000. Step 2: After second year decrease of 20%: Salary = 60,000 × 0.80 = ₹48,000. Step 3: Net change = 48,000 - 50,000 = -₹2,000, which is a 4% decrease.

Question 20

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. Profit % = (160/800) × 100 = 20%.

Question 21

In a school, 40% of students are boys. If 25% of boys and 10% of girls failed an exam, what percentage of the total student population failed?

Accepted Answer

Step 1: Assume total students = 100. Boys = 40, Girls = 60. Step 2: Boys who failed = 25% of 40 = 10. Girls who failed = 10% of 60 = 6. Step 3: Total failed = 10 + 6 = 16. Percentage failed = (16/100) × 100 = 16%.

SSC CHSL Percentage Word Problems

SSC CHSL Percentage Word Problems — Past Exam Questions

Percentage Word Problems— Rules & Concept

Key Points to Remember

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Percentage Word Problems — Practice Questions

60-Second Revision — Percentage Word Problems