Question 1

A student scored 72 marks out of 120 in an exam. What is the percentage score?

Accepted Answer

Step 1: Use the formula Percentage = (Obtained/Total) × 100. Step 2: Percentage = (72/120) × 100. Step 3: Simplify: (72/120) = (3/5) = 0.60. Step 4: 0.60 × 100 = 60%. Therefore, the percentage score is 60%.

Question 2

A book's price was reduced by 30% and now costs ₹490. What was the original price?

Accepted Answer

Step 1: Let original price = x. After 30% reduction, price = 70% of x. Step 2: 70% of x = 490. Step 3: (70/100) × x = 490. Step 4: x = 490 × (100/70) = 490 × (10/7) = 700. Therefore, the original price was ₹700.

Question 3

A shopkeeper marks an item at ₹500. He offers a discount of 15% on the marked price. What is the selling price?

Accepted Answer

Step 1: Marked Price (MP) = ₹500. Step 2: Discount = 15% of 500 = 0.15 × 500 = ₹75. Step 3: Selling Price (SP) = MP − Discount = 500 − 75 = ₹425. Therefore, the answer is ₹425.

Question 4

What is 25% of 480?

Accepted Answer

Step 1: Use the formula Percentage = (Percent/100) × Base. Step 2: 25% of 480 = (25/100) × 480 = 0.25 × 480 = 120. Therefore, the answer is 120.

Question 5

A shopkeeper marks an item at ₹500. He offers a discount of 12% on the marked price. What is the selling price of the item?

Accepted Answer

Step 1: Marked Price (MP) = ₹500. Step 2: Discount = 12% of ₹500 = (12/100) × 500 = ₹60. Step 3: Selling Price (SP) = MP − Discount = 500 − 60 = ₹440. Therefore, the selling price is ₹440.

Question 6

The price of a commodity increased by 25%. If the new price is ₹750, what was the original price?

Accepted Answer

Step 1: Let the original price = x. Step 2: After 25% increase, new price = x + 0.25x = 1.25x. Step 3: Given that 1.25x = 750, so x = 750 ÷ 1.25 = 600. Therefore, the original price was ₹600.

Question 7

In an examination, a student scored 72% and obtained 360 marks. What is the total marks of the examination?

Accepted Answer

Step 1: Let total marks = x. Step 2: 72% of x = 360, so 0.72x = 360. Step 3: Solve for x: x = 360 ÷ 0.72 = 500. Therefore, the total marks is 500.

Question 8

A shirt costs ₹800. Its price is increased by 20%. What is the new price?

Accepted Answer

Step 1: Original price = ₹800. Step 2: Increase = 20% of 800 = (20/100) × 800 = ₹160. Step 3: New price = 800 + 160 = ₹960. Therefore, the new price is ₹960.

Question 9

If 45% of a number is 360, what is 20% of that number?

Accepted Answer

Step 1: Let the number be x. Then 45% of x = 360, so 0.45x = 360. Step 2: Solve for x: x = 360 ÷ 0.45 = 800. Step 3: Find 20% of 800: 0.20 × 800 = 160. Therefore, the answer is 160.

Question 10

In a class of 200 students, 45% are boys. How many girls are there?

Accepted Answer

Step 1: Total students = 200. Boys = 45% of 200 = (45/100) × 200 = 90. Step 2: Girls = Total - Boys = 200 - 90 = 110. Therefore, there are 110 girls.

Question 11

If 15% of a number is 45, what is the number?

Accepted Answer

Step 1: Let the number be x. Then 15% of x = 45. Step 2: (15/100) × x = 45. Step 3: x = 45 × (100/15) = 45 × (20/3) = 300. Therefore, the number is 300.

Question 12

A shopkeeper marks up the cost price of an item by 40%. He then offers a discount of 10% on the marked price. If the cost price is ₹500, what is his profit percentage?

Accepted Answer

Step 1: Calculate marked price = Cost Price + 40% of CP = 500 + (40/100 × 500) = 500 + 200 = ₹700. Step 2: Calculate selling price after 10% discount = 700 - (10/100 × 700) = 700 - 70 = ₹630. Step 3: Calculate profit = SP - CP = 630 - 500 = ₹130. Step 4: Profit percentage = (Profit/CP) × 100 = (130/500) × 100 = 26%. Therefore, the answer is 26%.

Question 13

A number is increased by 25%. If the new number is 500, what was the original number?

Accepted Answer

Step 1: Let original number = x. Step 2: x + 25% of x = 500. Step 3: x(1 + 0.25) = 500. Step 4: 1.25x = 500. Step 5: x = 500/1.25 = 400.

Question 14

A shopkeeper marks an item at ₹500. He offers a discount of 12% on the marked price. What is the selling price?

Accepted Answer

Step 1: Marked Price = ₹500. Step 2: Discount = 12% of 500 = (12/100) × 500 = ₹60. Step 3: Selling Price = 500 − 60 = ₹440.

Question 15

A product's price was reduced by 15%, and then the reduced price was increased by 15%. What is the net percentage change from the original price?

Accepted Answer

Step 1: Let original price = ₹100. Step 2: After 15% reduction: 100 × 0.85 = ₹85. Step 3: After 15% increase on ₹85: 85 × 1.15 = ₹97.75. Step 4: Net change = 97.75 − 100 = −₹2.25. Step 5: Net percentage change = (−2.25/100) × 100 = −2.25% (a decrease).

Question 16

The price of petrol increased by 20% and then decreased by 10%. What is the net percentage change?

Accepted Answer

Step 1: Let original price = ₹100. Step 2: After 20% increase: 100 × 1.20 = ₹120. Step 3: After 10% decrease: 120 × 0.90 = ₹108. Step 4: Net change = 108 − 100 = ₹8. Step 5: Net percentage change = (8/100) × 100 = 8%.

Question 17

A student scored marks in three subjects: 75 out of 100 in Maths, 80 out of 100 in English, and 65 out of 100 in Science. What is the overall percentage scored by the student?

Accepted Answer

Step 1: Total marks obtained = 75 + 80 + 65 = 220. Step 2: Total maximum marks = 100 + 100 + 100 = 300. Step 3: Percentage = (220 / 300) × 100 = 73.33%. Therefore, the answer is 73.33%.

Question 18

In an examination, 65% of students passed. If 455 students passed, how many students appeared in total?

Accepted Answer

Step 1: Let total students = x. Step 2: 65% of x = 455. Step 3: (65/100) × x = 455. Step 4: x = 455 × (100/65) = 455 × (20/13) = 35 × 20 = 700.

Question 19

The price of a commodity increased by 20%, and then decreased by 10%. What is the net percentage change in the price?

Accepted Answer

Step 1: Let original price = ₹100. Step 2: After 20% increase: Price = 100 + 20 = ₹120. Step 3: After 10% decrease on ₹120: Decrease = (10/100) × 120 = ₹12. Step 4: Final price = 120 − 12 = ₹108. Step 5: Net change = 108 − 100 = ₹8 (increase). Step 6: Net percentage change = (8/100) × 100 = 8%.

Question 20

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 weighted average percentage?

Accepted Answer

Step 1: Weighted average = (Score₁ × Weight₁ + Score₂ × Weight₂) / (Weight₁ + Weight₂). Step 2: = (72 × 40 + 88 × 60) / (40 + 60). Step 3: = (2880 + 5280) / 100. Step 4: = 8160 / 100 = 81.6%.

Question 21

In an examination, a student scored 75% marks and obtained 300 marks. What are the total marks for the examination?

Accepted Answer

Step 1: Let total marks = x. Step 2: 75% of x = 300. Step 3: (75/100) × x = 300. Step 4: x = 300 × (100/75) = 300 × (4/3) = 400.

Question 22

A container has 120 litres of a mixture containing 40% alcohol. How many litres of pure alcohol must be added to make the alcohol content 60%?

Accepted Answer

Step 1: Current mixture = 120 litres with 40% alcohol. Step 2: Current alcohol = 40% of 120 = 0.40 × 120 = 48 litres. Step 3: Let x litres of pure alcohol be added. Step 4: New total volume = 120 + x litres. Step 5: New alcohol content = 48 + x litres. Step 6: For 60% concentration: (48 + x)/(120 + x) = 0.60. Step 7: 48 + x = 0.60(120 + x) = 72 + 0.60x. Step 8: 48 + x − 0.60x = 72. Step 9: 0.40x = 24. Step 10: x = 60 litres.

Question 23

A student scored 72% in English, 68% in Mathematics, and 80% in Science. The maximum marks for each subject are 150, 120, and 100 respectively. What is the overall percentage of marks obtained across all three subjects?

Accepted Answer

Step 1: English: 72% of 150 = 0.72 × 150 = 108 marks. Step 2: Mathematics: 68% of 120 = 0.68 × 120 = 81.6 marks. Step 3: Science: 80% of 100 = 0.80 × 100 = 80 marks. Step 4: Total marks obtained = 108 + 81.6 + 80 = 269.6 marks. Step 5: Total maximum marks = 150 + 120 + 100 = 370 marks. Step 6: Overall percentage = (269.6/370) × 100 = 72.86% ≈ 72.9% or 73% (rounded).

Question 24

A shopkeeper marks up goods by 60% above cost price. He then offers a discount of 25% on the marked price during a sale. Later, he realizes his profit margin is lower than expected and increases the selling price by 20%. What is his final profit percentage?

Accepted Answer

Step 1: Let cost price = 100. Marked price = 100 + 60% of 100 = 160. Step 2: After 25% discount on marked price, selling price = 160 − 25% of 160 = 160 − 40 = 120. Step 3: He increases this selling price by 20%, new selling price = 120 + 20% of 120 = 120 + 24 = 144. Step 4: Profit = 144 − 100 = 44. Profit percentage = (44/100) × 100 = 44%.

Question 25

A person's salary is increased by 25% in January and then decreased by 20% in February. If his salary in February is ₹12,000, what was his original salary in December?

Accepted Answer

Step 1: Let original salary (December) = S. Step 2: After 25% increase in January: Salary = S × 1.25. Step 3: After 20% decrease in February: Salary = S × 1.25 × 0.80 = S × 1.00. Step 4: February salary = S × 1.00 = 12,000. Step 5: S = 12,000. Step 6: Verification: 12,000 × 1.25 = 15,000 (January); 15,000 × 0.80 = 12,000 (February). ✓

Question 26

A quantity increases by 20%, then decreases by 25%, and finally increases by 10%. What is the net percentage change from the original quantity?

Accepted Answer

Step 1: Let original quantity = 100. Step 2: After 20% increase: 100 × 1.20 = 120. Step 3: After 25% decrease: 120 × 0.75 = 90. Step 4: After 10% increase: 90 × 1.10 = 99. Step 5: Net change = 99 − 100 = −1. Step 6: Net percentage change = (−1/100) × 100 = −1%.

Question 27

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. Step 2: Marked Price (MP) = 800 + (60% of 800) = 800 + 480 = ₹1280. Step 3: Discount = 25% of 1280 = 0.25 × 1280 = ₹320. Step 4: Selling Price (SP) = 1280 − 320 = ₹960. Step 5: Profit = SP − CP = 960 − 800 = ₹160. Step 6: Profit % = (160/800) × 100 = 20%.

Question 28

The price of a commodity increases by 20% in the first year and decreases by 15% in the second year. If the final price is ₹1224, what was the original price?

Accepted Answer

Step 1: Let original price = P. Step 2: After 20% increase in year 1: Price = P × 1.20. Step 3: After 15% decrease in year 2: Price = P × 1.20 × 0.85 = P × 1.02. Step 4: Final price = P × 1.02 = 1224. Step 5: P = 1224 ÷ 1.02 = 1200. Step 6: Verification: 1200 × 1.20 = 1440; 1440 × 0.85 = 1224. ✓

Question 29

In an election, candidate A received 45% of votes, candidate B received 35% of votes, and the remaining votes were invalid. If the total number of valid votes was 8000, how many invalid votes were cast?

Accepted Answer

Step 1: Candidate A received 45% of total votes. Candidate B received 35% of total votes. Step 2: Valid votes = 45% + 35% = 80% of total votes. Step 3: Invalid votes = 100% − 80% = 20% of total votes. Step 4: If valid votes = 8000, then 80% of total = 8000. Step 5: Total votes = 8000 ÷ 0.80 = 10,000. Step 6: Invalid votes = 20% of 10,000 = 0.20 × 10,000 = 2000.

Question 30

A shopkeeper marks the price of an item at ₹500. He offers a discount of 12% on the marked price. What is the selling price of the item?

Accepted Answer

Step 1: Marked Price (MP) = ₹500. Step 2: Discount = 12% of ₹500 = (12/100) × 500 = ₹60. Step 3: Selling Price (SP) = MP − Discount = 500 − 60 = ₹440. Therefore, the selling price is ₹440.

Question 31

A student scored 72 marks out of 120 in an exam. What is his percentage score?

Accepted Answer

Step 1: Marks obtained = 72, Total marks = 120. Step 2: Percentage = (Marks obtained ÷ Total marks) × 100 = (72 ÷ 120) × 100. Step 3: Simplify: (72 ÷ 120) = 0.6, so 0.6 × 100 = 60%. Therefore, the percentage score is 60%.

Question 32

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

Accepted Answer

Step 1: Marked Price (MP) = ₹500. Step 2: Discount = 20% of 500 = 0.20 × 500 = ₹100. Step 3: Selling Price (SP) = MP − Discount = 500 − 100 = ₹400. Therefore, the selling price is ₹400.

Question 33

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

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) = 9000/18 = 500. Therefore, the total marks were 500.

Question 34

In an exam, 65% of students passed. If 260 students passed, how many students took the exam?

Accepted Answer

Step 1: Let total students = x. Step 2: 65% of x = 260. Step 3: (65/100) × x = 260. Step 4: x = 260 × (100/65) = 260 × (20/13) = 5200/13 = 400. Therefore, 400 students took the exam.

Question 35

A shirt costs ₹800. Its price is increased by 20%. What is the new price?

Accepted Answer

Step 1: Original price = ₹800. Step 2: Increase = 20% of 800 = (20/100) × 800 = 160. Step 3: New price = 800 + 160 = ₹960. Therefore, the new price is ₹960.

Question 36

If 15% of a number is 45, what is the number?

Accepted Answer

Step 1: Let the number be x. Then 15% of x = 45. Step 2: (15/100) × x = 45. Step 3: x = 45 × (100/15) = 45 × (20/3) = 900/3 = 300. Therefore, the number is 300.

Question 37

What is 25% of 480?

Accepted Answer

Step 1: Use the percentage formula: Percentage of a number = (Percentage/100) × Number. Step 2: 25% of 480 = (25/100) × 480 = 0.25 × 480 = 120. Therefore, the answer is 120.

Question 38

In a class of 80 students, 35% are girls. How many boys are there in the class?

Accepted Answer

Step 1: Total students = 80. Girls = 35% of 80 = 0.35 × 80 = 28. Step 2: Boys = Total − Girls = 80 − 28 = 52. Therefore, there are 52 boys in the class.

Question 39

If 45% of a number is 360, what is 25% of that number?

Accepted Answer

Step 1: Let the number be x. Then 45% of x = 360, so 0.45x = 360. Step 2: Solve for x: x = 360 ÷ 0.45 = 800. Step 3: Find 25% of 800: 0.25 × 800 = 200. Therefore, the answer is 200.

Question 40

A book's price is reduced from ₹500 to ₹400. What is the percentage decrease?

Accepted Answer

Step 1: Original price = ₹500, New price = ₹400. Step 2: Decrease = 500 - 400 = ₹100. Step 3: Percentage decrease = (Decrease/Original) × 100 = (100/500) × 100 = 20%. Therefore, the percentage decrease is 20%.

Question 41

In an examination, a student scored 72% marks and obtained 360 marks. What are the total marks of the examination?

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) = 500. Therefore, total marks = 500.

Question 42

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

Accepted Answer

Step 1: Let original number = 100. Step 2: After 25% increase: 100 + 25 = 125. Step 3: Decrease 125 by 20%: 125 − (20% of 125) = 125 − 25 = 100. Step 4: Net change = 100 − 100 = 0. Step 5: Net percentage change = (0/100) × 100 = 0%. Therefore, there is no net change.

Question 43

A number is increased by 30%, and then the result is decreased by 30%. Is the final number greater than, less than, or equal to the original number?

Accepted Answer

Step 1: Let original number = 100. Step 2: After 30% increase = 100 × 1.30 = 130. Step 3: After 30% decrease on 130 = 130 × 0.70 = 91. Step 4: Final number (91) < Original number (100). The final number is 9% less than the original.

Question 44

A shopkeeper marks up the cost price of an item by 40%. He then offers a discount of 10% on the marked price. If the cost price is ₹500, what is his profit percentage?

Accepted Answer

Step 1: Calculate marked price = Cost Price + 40% of CP = 500 + (40/100 × 500) = 500 + 200 = ₹700. Step 2: Calculate selling price after 10% discount = 700 - (10/100 × 700) = 700 - 70 = ₹630. Step 3: Calculate profit = SP - CP = 630 - 500 = ₹130. Step 4: Profit percentage = (Profit/CP) × 100 = (130/500) × 100 = 26%.

Question 45

In an examination, 65% of students passed. If 455 students passed, how many students appeared in total?

Accepted Answer

Step 1: Let total students = x. Step 2: 65% of x = 455. Step 3: (65/100) × x = 455. Step 4: x = 455 × (100/65) = 455 × (20/13) = 35 × 20 = 700. Therefore, total students = 700.

Question 46

A shopkeeper marks an item at ₹500. He offers a discount of 12% on the marked price. What is the selling price?

Accepted Answer

Step 1: Marked Price (MP) = ₹500. Step 2: Discount = 12% of 500 = (12/100) × 500 = ₹60. Step 3: Selling Price (SP) = MP − Discount = 500 − 60 = ₹440. Therefore, the answer is ₹440.

Question 47

A shopkeeper buys goods for ₹800 and sells them at a profit of 35%. What is the selling price?

Accepted Answer

Step 1: Cost Price (CP) = ₹800. Step 2: Profit% = 35%. Step 3: Profit = 35% of 800 = (35/100) × 800 = ₹280. Step 4: Selling Price (SP) = CP + Profit = 800 + 280 = ₹1080.

Question 48

A student's marks increased from 45 to 54. What is the percentage increase in marks?

Accepted Answer

Step 1: Original marks = 45. Step 2: New marks = 54. Step 3: Increase = 54 − 45 = 9. Step 4: Percentage increase = (Increase / Original) × 100 = (9 / 45) × 100 = 20%.

Question 49

The price of a commodity increases by 25% and then decreases by 20%. What is the net percentage change in the price?

Accepted Answer

Step 1: Let original price = ₹100. Step 2: After 25% increase = 100 + 25 = ₹125. Step 3: After 20% decrease on ₹125 = 125 − (20% of 125) = 125 − 25 = ₹100. Step 4: Net change = 100 − 100 = 0. Net percentage change = 0%.

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