Question 1

A number is increased by 25%, then decreased by 20%. If the final result is 600, what is the original number?

Accepted Answer

Step 1: Let original number = x. After 25% increase: x × 1.25. Step 2: After 20% decrease: (x × 1.25) × 0.80 = x × 1.00 = x. Step 3: x × 1.00 = 600, so x = 600.

Question 2

A person spends 30% of his income on rent, 25% on food, and 15% on transport. He saves the remaining amount. If his savings are ₹18,000, what is his total income?

Accepted Answer

Step 1: Total spending percentage = 30% + 25% + 15% = 70%. Step 2: Savings percentage = 100% - 70% = 30%. Step 3: If 30% of income = ₹18,000, then income = 18,000 ÷ 0.30 = ₹60,000.

Question 3

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. Commerce students passing = 30% of 35 = 10.5. Step 3: Total passing = 8 + 10.5 = 18.5. Percentage of total = (18.5/100) × 100 = 18.5%.

Question 4

A mobile phone costs ₹15,000. During a sale, it is offered at 18% discount. What is the sale price of the mobile phone?

Accepted Answer

Step 1: Original price = ₹15,000. Discount = 18%. Step 2: Discount amount = 18% of 15,000 = 0.18 × 15,000 = 2,700. Step 3: Sale price = 15,000 - 2,700 = 12,300. Therefore, the sale price is ₹12,300.

Question 5

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. Student scored 72% of T = 360. Step 2: 0.72 × T = 360. Step 3: T = 360 ÷ 0.72 = 500. Therefore, total marks = 500.

Question 6

The price of a book increased from ₹200 to ₹250. What is the percentage increase in price?

Accepted Answer

Step 1: Original price = ₹200, New price = ₹250. Step 2: Increase = 250 - 200 = ₹50. Step 3: Percentage increase = (Increase ÷ Original price) × 100 = (50 ÷ 200) × 100 = 0.25 × 100 = 25%. Therefore, percentage increase is 25%.

Question 7

A factory produces 5000 units per month. If production increases by 12%, how many units will be produced in the next month?

Accepted Answer

Step 1: Current production = 5000 units. Step 2: Increase = 12% of 5000 = 0.12 × 5000 = 600 units. Step 3: New production = 5000 + 600 = 5600 units. Therefore, 5600 units will be produced in the next month.

Question 8

A shopkeeper sells a shirt for ₹480, which is 20% more than its cost price. What is the cost price of the shirt?

Accepted Answer

Step 1: Let cost price = CP. Selling price = 480. Step 2: SP = CP + 20% of CP = CP(1 + 0.20) = 1.20 × CP. Step 3: 1.20 × CP = 480. Step 4: CP = 480 ÷ 1.20 = 400. Therefore, cost price is ₹400.

Question 9

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: Candidate A received 55% of 8000 = 0.55 × 8000 = 4400 votes. Step 2: Candidate B received remaining votes = 8000 - 4400 = 3600 votes. Step 3: Difference = 4400 - 3600 = 800 votes. Therefore, A received 800 more votes than B.

Question 10

A product's price was reduced by 20%, and then reduced again by 10%. What is the overall percentage reduction from the original price?

Accepted Answer

Step 1: Let original price = ₹100. Step 2: After first reduction of 20%: Price = 100 − 20 = ₹80. Step 3: After second reduction of 10% on ₹80: Reduction = (10/100) × 80 = ₹8. Step 4: Final price = 80 − 8 = ₹72. Step 5: Overall reduction = 100 − 72 = ₹28. Step 6: Overall percentage reduction = (28/100) × 100 = 28%. Therefore, the overall percentage reduction is 28%.

Question 11

In an examination, a student scored 75% of the total marks. 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 = (75/100) × 320 = 0.75 × 320 = 240. Therefore, the student scored 240 marks.

Question 12

A company's revenue increased from ₹40 lakhs to ₹50 lakhs. What is the percentage increase in revenue?

Accepted Answer

Step 1: Initial revenue = ₹40 lakhs. Step 2: Final revenue = ₹50 lakhs. Step 3: Increase = 50 − 40 = ₹10 lakhs. Step 4: Percentage increase = (Increase/Initial) × 100 = (10/40) × 100 = 25%. Therefore, the percentage increase is 25%.

Question 13

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 14

A student's marks increased from 60 to 75. What is the percentage increase in marks?

Accepted Answer

Step 1: Initial marks = 60. Step 2: Final marks = 75. Step 3: Increase in marks = 75 − 60 = 15. Step 4: Percentage increase = (Increase/Initial) × 100 = (15/60) × 100 = 25%. Therefore, the percentage increase is 25%.

Question 15

A bank account had ₹8,000 initially. After one year, it grew by 15%. How much money is in the account now?

Accepted Answer

Step 1: Initial amount = ₹8,000. Step 2: Growth percentage = 15%. Step 3: Growth amount = (15/100) × 8,000 = ₹1,200. Step 4: Final amount = 8,000 + 1,200 = ₹9,200. Therefore, the account now has ₹9,200.

Question 16

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 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%.

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