Question 1

A student scored 450 marks out of 600 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 = (450 / 600) × 100 = 0.75 × 100 = 75%. Therefore, the student scored 75%.

Question 2

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

Accepted Answer

Step 1: Let cost price (CP) = ₹100. Step 2: Marked price (MP) = 100 + 40% of 100 = ₹140. Step 3: Discount = 20% of 140 = ₹28. Step 4: Selling price (SP) = 140 − 28 = ₹112. Step 5: Profit = SP − CP = 112 − 100 = ₹12. Step 6: Profit % = (12/100) × 100 = 12%. Therefore, the answer is 12%.

Question 3

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

Accepted Answer

Step 1: Cost Price (CP) = ₹800. Marked Price (MP) = CP + 40% of CP = 800 + 0.40(800) = 800 + 320 = ₹1120. Step 2: Selling Price (SP) = MP − 25% of MP = 1120 − 0.25(1120) = 1120 − 280 = ₹840. Step 3: Profit = SP − CP = 840 − 800 = ₹40. Step 4: Profit % = (Profit/CP) × 100 = (40/800) × 100 = 5%. Therefore, the profit percentage is 5%.

Question 4

In an election between two candidates, the winning candidate got 60% of the total votes cast. If the winning candidate won by 480 votes, what was the total number of votes cast?

Accepted Answer

Step 1: Let total votes = V. Winning candidate got 60% of V, losing candidate got 40% of V. Step 2: Difference = 60% - 40% = 20% of V = 480. Step 3: V = 480 / 0.20 = 2400. Therefore, total votes cast = 2400.

Question 5

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 of the item is ₹800, what is his profit percentage?

Accepted Answer

Step 1: Cost Price (CP) = ₹800. Marked Price (MP) = CP + 40% of CP = 800 + (40/100 × 800) = 800 + 320 = ₹1120. Step 2: Selling Price (SP) = MP − 25% of MP = 1120 − (25/100 × 1120) = 1120 − 280 = ₹840. Step 3: Profit = SP − CP = 840 − 800 = ₹40. Step 4: Profit % = (Profit/CP) × 100 = (40/800) × 100 = 5%. Therefore, the profit percentage is 5%.

Question 6

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

Accepted Answer

Step 1: 15% failed in both, so 85% passed in at least one subject. Step 2: Using the formula: Passed in both = (Passed in English + Passed in Maths) - Passed in at least one. Step 3: Passed in both = 65% + 75% - 85% = 140% - 85% = 55%.

Question 7

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 8

A student scores 45% in an exam and fails by 15 marks. If he had scored 55%, he would have passed by 5 marks. What is the passing mark for the exam?

Accepted Answer

Step 1: Let total marks = x and passing mark = p. From condition 1: 0.45x = p - 15. From condition 2: 0.55x = p + 5. Step 2: Subtract first from second: 0.10x = 20, so x = 200. Step 3: Substitute back: 0.45(200) = p - 15, so 90 = p - 15, thus p = 105.

Question 9

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

Accepted Answer

Step 1: Let total students = 100. Failed in Math = 35, Failed in English = 28, Failed in both = 10. Step 2: Using set theory: Failed in at least one subject = 35 + 28 - 10 = 53. Step 3: Passed both = 100 - 53 = 47%.

Question 10

A student scored 65% marks in English and 72% marks 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 = (English score × English weightage) + (Mathematics score × Mathematics weightage). Step 2: Weighted score = (65 × 0.40) + (72 × 0.60) = 26 + 43.2 = 69.2%.

Question 11

A shopkeeper marks up the price of an item by 40%. If he then gives a discount of 10% on the marked price, what is his profit percentage?

Accepted Answer

Step 1: Let the cost price be ₹100. Step 2: Marked price = 100 + 40% of 100 = ₹140. Step 3: Selling price after 10% discount = 140 − 10% of 140 = 140 − 14 = ₹126. Step 4: Profit = 126 − 100 = ₹26. Step 5: Profit percentage = (26/100) × 100 = 26%. Therefore, the answer is 26%.

Question 12

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, how many more votes did A receive than B?

Accepted Answer

Step 1: Votes for A = 55% of 8000 = 0.55 × 8000 = 4400. Step 2: Votes for B = 45% of 8000 = 0.45 × 8000 = 3600. Step 3: Difference = 4400 - 3600 = 800.

Question 13

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 14

A shopkeeper marks an item at ₹500. He offers a discount of 20% on the marked price. What is the selling price?

Accepted Answer

Step 1: Marked Price = ₹500. Step 2: Discount = 20% of ₹500 = (20/100) × 500 = ₹100. Step 3: Selling Price = Marked Price − Discount = 500 − 100 = ₹400.

Question 15

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

Accepted Answer

Step 1: Let total marks = x. Step 2: 72% of x = 360. Step 3: (72/100) × x = 360. Step 4: x = 360 × (100/72) = 360 × (25/18) = 20 × 25 = 500.

Question 16

The population of a town decreased by 12% in one year. If the population is now 22,000, what was it a year ago?

Accepted Answer

Step 1: Current population = 22,000. Step 2: Population decreased by 12%, so current = 88% of original. Step 3: Let original population = x. Step 4: 88% of x = 22,000. Step 5: (88/100) × x = 22,000. Step 6: x = 22,000 × (100/88) = 22,000 × (25/22) = 1000 × 25 = 25,000.

Question 17

The price of a commodity increases by 20%. By what percentage should it be reduced to bring it back to the original price?

Accepted Answer

Step 1: Let original price = 100. After 20% increase: 100 + 20 = 120. Step 2: To return to 100 from 120, reduction needed = 20. Step 3: Reduction percentage = (20/120) × 100 = 16.67% (or 16⅔%).

Question 18

The price of petrol increased by 20%. A consumer wants to spend the same amount of money as before. By what percentage should he reduce his consumption?

Accepted Answer

Step 1: Let original price = P and original consumption = C. Original expenditure = P × C. Step 2: New price = 1.2P. For same expenditure: 1.2P × C' = P × C, so C' = C/1.2 = 5C/6. Step 3: Reduction in consumption = C - 5C/6 = C/6. Percentage reduction = (C/6)/C × 100 = 16.67% ≈ 16⅔%.

Question 19

A student scored 45% marks in an examination and failed by 36 marks. Another student scored 65% marks and passed by 24 marks. What is the passing percentage?

Accepted Answer

Step 1: Let total marks = x. First student: 45% of x = passing marks - 36. Second student: 65% of x = passing marks + 24. Step 2: From both equations: 0.45x = P - 36 and 0.65x = P + 24. Step 3: Subtracting: 0.65x - 0.45x = (P + 24) - (P - 36). 0.20x = 60. x = 300. Step 4: Passing marks = 0.45(300) + 36 = 135 + 36 = 171. Passing percentage = (171/300) × 100 = 57%.

Question 20

A number is increased by 25%, and then the result is decreased by 20%. What is the net change in the original number?

Accepted Answer

Step 1: Let original number = 100. After 25% increase: 100 + 25 = 125. Step 2: After 20% decrease on 125: 125 - (20% of 125) = 125 - 25 = 100. Step 3: Net change = 100 - 100 = 0. Net change percentage = 0%.

Question 21

A shopkeeper bought an item for ₹600 and sold it at a profit of 25%. What is the selling price?

Accepted Answer

Step 1: Cost Price (CP) = ₹600. Step 2: Profit percentage = 25%. Step 3: Profit amount = 25% of ₹600 = (25/100) × 600 = ₹150. Step 4: Selling Price (SP) = CP + Profit = 600 + 150 = ₹750.

Question 22

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

Accepted Answer

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

Question 23

In an examination, 65% of students passed. If 520 students passed, how many students appeared in total?

Accepted Answer

Step 1: Let total students = x. Step 2: 65% of x = 520. Step 3: (65/100) × x = 520. Step 4: x = 520 × (100/65) = 520 × (20/13) = 40 × 20 = 800.

Question 24

A mobile phone's price increased by 15% from last year. If the price last year was ₹8000, what is the current price?

Accepted Answer

Step 1: Last year's price = ₹8000. Step 2: Percentage increase = 15%. Step 3: Increase amount = 15% of ₹8000 = (15/100) × 8000 = ₹1200. Step 4: Current price = 8000 + 1200 = ₹9200.

Question 25

A salary is increased by 15% in the first year and by 10% in the second year. What is the total percentage increase over the two years?

Accepted Answer

Step 1: Let original salary = 100. After 15% increase: 100 × 1.15 = 115. Step 2: After 10% increase on 115: 115 × 1.10 = 126.5. Step 3: Total increase = 126.5 - 100 = 26.5. Total percentage increase = 26.5%.

CDS Percentage Word Problems

CDS Percentage Word Problems — Past Exam Questions

Percentage Word Problems — Practice Questions