Question 1

A student scored 72% in an exam and obtained 360 marks. What are the total marks of the exam?

Accepted Answer

Step 1: Let total marks = T. Step 2: 72% of T = 360. Step 3: 0.72 × T = 360. Step 4: T = 360 ÷ 0.72 = 500. Therefore, the total marks of the exam are 500.

Question 2

A company's profit increased from ₹50,000 to ₹65,000. What is the percentage increase in profit?

Accepted Answer

Step 1: Original profit = ₹50,000, New profit = ₹65,000. Step 2: Increase = 65,000 − 50,000 = ₹15,000. Step 3: Percentage increase = (15,000 ÷ 50,000) × 100 = 0.30 × 100 = 30%. Therefore, the percentage increase in profit is 30%.

Question 3

A shopkeeper sells an item at ₹480, which is 20% more than its cost price. What is the cost price of the item?

Accepted Answer

Step 1: Let cost price = CP. Step 2: Selling price = CP + 20% of CP = 1.20 × CP. Step 3: 1.20 × CP = 480. Step 4: CP = 480 ÷ 1.20 = 400. Therefore, the cost price is ₹400.

Question 4

In an exam, 65% of students passed. If 455 students passed, how many students appeared for the exam?

Accepted Answer

Step 1: Let total students = T. Step 2: 65% of T = 455. Step 3: 0.65 × T = 455. Step 4: T = 455 ÷ 0.65 = 700. Therefore, 700 students appeared for the exam.

Question 5

In an examination, 35% of students failed in Hindi, 28% failed in English, and 20% failed in both subjects. What percentage of students passed in both subjects?

Accepted Answer

Step 1: Use the formula: Failed in at least one = Failed in Hindi + Failed in English - Failed in both. Step 2: Failed in at least one = 35 + 28 - 20 = 43%. Step 3: Passed in both = 100 - 43 = 57%.

Question 6

A shopkeeper marks his goods at 40% above the cost price. He then offers 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 7

A student scored 65% marks in one exam and 75% marks in another exam. If the first exam had 80 questions and the second had 120 questions, what is the overall percentage of marks obtained?

Accepted Answer

Step 1: Marks in first exam = 65% of 80 = 0.65 × 80 = 52. Step 2: Marks in second exam = 75% of 120 = 0.75 × 120 = 90. Step 3: Total marks obtained = 52 + 90 = 142. Step 4: Total questions = 80 + 120 = 200. Step 5: Overall percentage = (142/200) × 100 = 71%.

Question 8

The price of petrol increased by 25% last month. This month, it decreased by 20%. If the current price is ₹84 per litre, what was the price two months ago?

Accepted Answer

Step 1: Let price two months ago = x. After 25% increase: x × 1.25. Step 2: After 20% decrease: x × 1.25 × 0.80 = x × 1.00. Step 3: x × 1.00 = 84. Step 4: x = 84.

Question 9

A company's revenue increased from ₹50 lakhs to ₹65 lakhs. In the same period, expenses increased from ₹30 lakhs to ₹39 lakhs. By what percentage did the profit increase?

Accepted Answer

Step 1: Initial profit = 50 - 30 = 20 lakhs. Step 2: Final profit = 65 - 39 = 26 lakhs. Step 3: Profit increase = 26 - 20 = 6 lakhs. Step 4: Percentage increase = (6/20) × 100 = 30%.

Question 10

In an election, Candidate A received 45% of votes, Candidate B received 35% of votes, and Candidate C received the remaining votes. If A won by 2,000 votes over B, how many votes did C receive?

Accepted Answer

Step 1: Let total votes = x. A's votes = 0.45x. B's votes = 0.35x. C's votes = 0.20x. Step 2: A won by 2,000 votes over B: 0.45x - 0.35x = 2,000. Step 3: 0.10x = 2,000. Step 4: x = 20,000. Step 5: C's votes = 0.20 × 20,000 = 4,000.

Question 11

A shopkeeper marks up goods by 60% above cost price. He then offers a discount of 25% on the marked price during a sale. If the cost price of an item is ₹400, what is his profit percentage?

Accepted Answer

Step 1: Cost Price (CP) = ₹400. Marked Price (MP) = 400 + (60% of 400) = 400 + 240 = ₹640. Step 2: Discount = 25% of 640 = 160. Selling Price (SP) = 640 - 160 = ₹480. Step 3: Profit = 480 - 400 = ₹80. Profit % = (80/400) × 100 = 20%.

Question 12

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 population passes the exam?

Accepted Answer

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

Question 13

A container has 200 litres of milk. Each day, 25% of the milk is removed and replaced with water. After 2 days, what is the percentage of milk in the container?

Accepted Answer

Step 1: Initial milk = 200 litres. Day 1: 25% removed = 50 litres. Milk remaining = 150 litres. Water added = 50 litres. Total = 200 litres. Step 2: Day 2: 25% of 200 = 50 litres removed (mixture contains 75% milk). Milk removed = 50 × 0.75 = 37.5 litres. Milk remaining = 150 - 37.5 = 112.5 litres. Step 3: Percentage = (112.5/200) × 100 = 56.25%.

SSC CPO Percentage Word Problems

Percentage Word Problems— Rules & Concept

Key Points to Remember

Exam-Specific Tips

Percentage Word Problems — Practice Questions

60-Second Revision — Percentage Word Problems