Percentage Practice Set 2 is designed as the next step after basic percentage practice. The questions here are more mixed and require you to identify the correct percentage relationship before calculating.
This set focuses on reverse percentage, comparison, successive percentage change, price-consumption, income-expenditure, ratio, marks, discount and other mixed arithmetic patterns that often cause mistakes under exam pressure.
If your basics are still weak, revise the Percentage Master Guide and complete Percentage Practice Set 1 before attempting this set.
How to Use Percentage Practice Set 2
- Attempt each question before reading the solution.
- Identify the base value before choosing a formula.
- Write one line explaining why your method is valid.
- Mark questions that require more than one percentage step.
- Repeat the set with a timer only after accuracy is stable.
Strategy for Mixed Percentage Questions
Set 2 is not mainly a calculation test. It checks whether you can recognise which percentage relationship is hidden inside the wording. Before choosing a formula, identify the original value, changed value, and the value being used as the comparison base.
For mixed questions, use this sequence:
- Write what represents 100%.
- Identify whether the percentage acts on the original or an updated value.
- Check whether the question asks for a value, a percentage, or a percentage-point change.
- Choose a multiplier, fraction, or direct formula only after the relationship is clear.
Three Traps to Watch for in Set 2
Changing base: if A is 40% more than B, reversing the comparison does not give 40% again because the base changes.
Successive changes: two percentage changes usually act on different values, so adding or subtracting the rates directly can be wrong.
Price and consumption: if expenditure must remain constant, price and quantity move in opposite directions, but by different percentage rates.
How to Decide Whether You Need Revision
After the set, group every mistake by cause: wrong concept, wrong base, calculation error, or careless reading. If several mistakes come from the same category, revise that topic before attempting the set again.
A higher score matters less than being able to explain why each method works. That is what makes the skill reliable when the numbers or wording change in an actual exam.
Question 1: Reverse Percentage After Increase
After a 25% increase, a number becomes 750. What was the original number?
- A. 560
- B. 580
- C. 600
- D. 625
Answer: C. 600
Explanation: 750 represents 125% of the original number. Original = 750 × 100/125 = 600.
Question 2: Reverse Percentage After Decrease
A price is reduced by 15% and becomes ₹1,700. What was the original price?
- A. ₹1,900
- B. ₹2,000
- C. ₹2,100
- D. ₹2,200
Answer: B. ₹2,000
Explanation: ₹1,700 is 85% of the original price. Original = 1,700 × 100/85 = ₹2,000.
Question 3: Reverse Comparison
A is 40% more than B. By what percentage is B less than A?
- A. 25%
- B. 28.57%
- C. 35%
- D. 40%
Answer: B. 28.57% approximately
Explanation: Let B = 100. Then A = 140. The difference is 40. Therefore B is 40/140 × 100 = 28.57% approximately less than A.
Question 4: Successive Increase
A quantity increases by 20% and then by another 25%. What is the overall percentage increase?
- A. 45%
- B. 48%
- C. 50%
- D. 52%
Answer: C. 50%
Explanation: Assume the original value is 100. After 20% increase → 120. After 25% increase → 150. Overall increase = 50%.
Question 5: Successive Decrease
A value decreases by 20% and then by 25%. What is the overall percentage decrease?
- A. 40%
- B. 42%
- C. 45%
- D. 50%
Answer: A. 40%
Explanation: Assume original = 100. After 20% decrease → 80. After 25% decrease → 60. Net decrease = 40%.
Question 6: Increase Followed by Decrease
A value increases by 30% and then decreases by 20%. What is the net percentage change?
- A. 2% increase
- B. 4% increase
- C. 6% increase
- D. 10% increase
Answer: B. 4% increase
Explanation: Assume original = 100. 100 → 130 → 104. The final value is 104, so net change = 4% increase.
Question 7: Price and Consumption
The price of a commodity increases by 20%. By what percentage must consumption be reduced so that expenditure remains unchanged?
- A. 15%
- B. 16.67%
- C. 18%
- D. 20%
Answer: B. 16.67% approximately
Explanation: Assume old price = 100 and consumption = 100. Expenditure = 10,000. New price = 120, so new consumption = 10,000/120 = 83.33 units approximately. Reduction = 16.67% approximately.
Question 8: Price Reduction and Consumption
The price of an item decreases by 20%. By what percentage can consumption increase while keeping expenditure unchanged?
- A. 20%
- B. 22%
- C. 25%
- D. 30%
Answer: C. 25%
Explanation: Assume old price = 100 and old consumption = 100. New price = 80. To keep expenditure at 10,000, new consumption = 10,000/80 = 125 units. Increase = 25%.
Question 9: Income and Expenditure
A person's income increases by 20% while expenditure increases by 10%. If the original income was ₹50,000 and expenditure was ₹40,000, what are the new savings?
- A. ₹14,000
- B. ₹16,000
- C. ₹18,000
- D. ₹20,000
Answer: B. ₹16,000
Explanation: New income = 50,000 × 1.20 = ₹60,000. New expenditure = 40,000 × 1.10 = ₹44,000. New savings = 60,000 - 44,000 = ₹16,000.
Question 10: Marks Required for a Target Percentage
An examination carries 600 marks. A student wants to score 75%. How many marks are required?
- A. 420
- B. 440
- C. 450
- D. 480
Answer: C. 450
Explanation: Required marks = 75% of 600 = 75/100 × 600 = 450.
Question 11: Percentage Increase in Marks
A student's score rises from 320 to 400. What is the percentage increase?
- A. 20%
- B. 22%
- C. 25%
- D. 28%
Answer: C. 25%
Explanation: Increase = 80. Percentage increase = 80/320 × 100 = 25%.
Question 12: Ratio to Percentage
The ratio of boys to girls in a class is 5:3. What percentage of the class are girls?
- A. 35%
- B. 37.5%
- C. 40%
- D. 42.5%
Answer: B. 37.5%
Explanation: Total parts = 5 + 3 = 8. Girls = 3/8 of the class. 3/8 × 100 = 37.5%.
Question 13: Finding Total from a Percentage
If 42 students represent 35% of a group, how many students are in the group?
- A. 100
- B. 110
- C. 120
- D. 140
Answer: C. 120
Explanation: Total = 42 × 100/35 = 120.
Question 14: Pass Percentage from Fail Count
Out of 800 candidates, 120 fail. What percentage of candidates pass?
- A. 80%
- B. 82%
- C. 85%
- D. 88%
Answer: C. 85%
Explanation: Candidates passing = 800 - 120 = 680. Pass percentage = 680/800 × 100 = 85%.
Question 15: Discount and Marked Price
An item marked at ₹2,500 is sold at a 12% discount. What is the selling price?
- A. ₹2,150
- B. ₹2,180
- C. ₹2,200
- D. ₹2,250
Answer: C. ₹2,200
Explanation: Discount = 12% of ₹2,500 = ₹300. Selling price = 2,500 - 300 = ₹2,200.
Question 16: Reverse Discount
After a 25% discount, an item costs ₹1,500. What was the marked price?
- A. ₹1,800
- B. ₹1,900
- C. ₹2,000
- D. ₹2,100
Answer: C. ₹2,000
Explanation: ₹1,500 is 75% of the marked price. Marked price = 1,500 × 100/75 = ₹2,000.
Question 17: Percentage Points
A success rate increases from 48% to 60%. What is the increase in percentage points?
- A. 10
- B. 12
- C. 20
- D. 25
Answer: B. 12 percentage points
Explanation: 60% - 48% = 12 percentage points. This is different from relative percentage increase.
Question 18: Relative Percentage Increase
A rate rises from 48% to 60%. What is the relative percentage increase?
- A. 20%
- B. 22%
- C. 25%
- D. 30%
Answer: C. 25%
Explanation: Increase = 12. Relative increase = 12/48 × 100 = 25%.
Question 19: Population Successive Change
A town's population increases by 10% in one year and by 20% the next year. What is the overall percentage increase?
- A. 30%
- B. 31%
- C. 32%
- D. 33%
Answer: C. 32%
Explanation: Assume population = 100. 100 → 110 → 132. Overall increase = 32%.
Question 20: Mixed Percentage Reasoning
In a class, 35% of students are girls. If there are 52 boys, what is the total number of students?
- A. 70
- B. 75
- C. 80
- D. 85
Answer: C. 80
Explanation: If 35% are girls, 65% are boys. 65% of total = 52. Total = 52 × 100/65 = 80.
What Makes Set 2 Different from Set 1?
Set 1 focuses on basic percentage patterns and direct application. Set 2 requires more interpretation, reverse calculation, multi-step reasoning and percentage relationships where the base changes.
If you found several questions difficult, revise the relevant topic rather than repeating the whole set blindly.
Use Percentage Word Problems for language-heavy questions, Percentage Mistakes for base-value errors, and Percentage Formulas for formula revision.
How to Review Your Score
- 17–20 correct: strong mixed-percentage control.
- 13–16 correct: good base, but revise weak patterns.
- 9–12 correct: mixed application still needs work.
- Below 9: return to concepts before timed practice.
Next Step
Return to the Percentage Master Guide for weak concepts, or practise mixed patterns in Exam-Based Percentage Questions.
For faster calculations, use Percentage Shortcuts and Percentage Speed Tricks.