Question 1

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 2

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 3

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 in both subjects?

Accepted Answer

Step 1: Students who failed in at least one subject = Failed in Maths + Failed in English - Failed in both = 35% + 28% - 10% = 53%. Step 2: Students who passed in both subjects = 100% - 53% = 47%.

Question 4

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

Accepted Answer

Step 1: Let the original number = 100. After 20% increase = 100 + 20 = 120. Step 2: After 20% decrease on 120 = 120 - (20% of 120) = 120 - 24 = 96. Step 3: Net change = 96 - 100 = -4. Net change percentage = (-4/100) × 100 = -4% (or 4% decrease).

Question 5

A student scored 65% in one exam and 75% in another exam. If the first exam has a weightage of 40% and the second exam has a weightage of 60%, what is the weighted average score?

Accepted Answer

Step 1: Weighted average = (Score₁ × Weight₁) + (Score₂ × Weight₂) = (65 × 0.40) + (75 × 0.60). Step 2: = 26 + 45 = 71%.

Question 6

The price of an item was reduced by 25%. By what percentage should the reduced price be increased to restore it to the original price?

Accepted Answer

Step 1: Let original price = 100. Reduced price = 100 - 25 = 75. Step 2: To restore to 100, increase needed = 100 - 75 = 25. Step 3: Percentage increase = (25/75) × 100 = 33.33% (or 33⅓%).

Question 7

The price of a commodity increased by 25% in the first year and then decreased by 20% in the second year. If the original price was ₹400, what is the final price after two years?

Accepted Answer

Step 1: Price after first year = 400 + 25% of 400 = 400 × 1.25 = ₹500. Step 2: Price after second year = 500 - 20% of 500 = 500 × 0.80 = ₹400. Step 3: Final price = ₹400.

Question 8

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 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.

Question 10

A student scored 72% in English and 68% 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 in English = 72 × 40% = 72 × 0.40 = 28.8. Step 2: Weighted score in Mathematics = 68 × 60% = 68 × 0.60 = 40.8. Step 3: Overall percentage = 28.8 + 40.8 = 69.6%.

Question 11

A person's salary is increased by 15%. If his new salary is ₹11,500, what was his original salary?

Accepted Answer

Step 1: Let original salary = x. New salary = x + 15% of x = 1.15x. Step 2: 1.15x = 11,500. Step 3: x = 11,500 ÷ 1.15 = ₹10,000.

Question 12

In a school, 60% of students are boys. If there are 240 boys, what is the total number of students in the school?

Accepted Answer

Step 1: Let total students = x. Boys = 60% of x = 0.60x. Step 2: 0.60x = 240. Step 3: x = 240 ÷ 0.60 = 400 students.

Question 13

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 ₹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 = 320. Step 4: Selling Price (SP) = 1280 - 320 = ₹960. Step 5: Profit = 960 - 800 = ₹160. Step 6: Profit % = (160/800) × 100 = 20%.

Question 14

A person's salary increases by 20% in the first year and then decreases by 20% in the second year. If his final salary is ₹9600, what was his original salary?

Accepted Answer

Step 1: Let original salary = S. Step 2: After 20% increase: Salary = S × 1.20 = 1.20S. Step 3: After 20% decrease on new salary: Salary = 1.20S × 0.80 = 0.96S. Step 4: Final salary = 0.96S = 9600. Step 5: S = 9600/0.96 = 10000. Therefore, original salary = ₹10000.

Question 15

A student scores 65% in one exam and 75% in another exam. If the first exam has a weightage of 40% and the second exam has a weightage of 60%, and he needs 70% overall to pass, by what percentage did he fall short or exceed the passing mark?

Accepted Answer

Step 1: Weighted average = (65 × 40% + 75 × 60%) = (26 + 45) = 71%. Step 2: Passing mark = 70%. Step 3: Excess = 71% - 70% = 1 percentage point. The student exceeded the passing mark by 1 percentage point.

Question 16

The price of a commodity increases by 25% in January and then decreases by 10% in February. In March, it increases by 20%. If the final price in March is ₹1350, what was the original price before January?

Accepted Answer

Step 1: Original price = P. Step 2: Jan: P × 1.25 = 1.25P. Step 3: Feb: 1.25P × 0.90 = 1.125P. Step 4: Mar: 1.125P × 1.20 = 1.35P = 1350. Step 5: P = 1350/1.35 = 1000.

SSC MTS Percentage Word Problems

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60-Second Revision — Percentage Word Problems