Percentage
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Solved Examples
Study MaterialSolved Examples – Percentage
Solved examples help students understand the practical application of Percentage concepts in competitive examinations. These examples are designed from basic to advanced level and cover important percentage problems frequently asked in SSC, Banking, Railway, CDS, NDA, CAT, UPSC, and placement aptitude tests.
Topics Covered in Solved Examples
- Basic Percentage Calculations
- Fraction to Percentage Conversion
- Percentage Increase and Decrease
- Successive Percentage Change
- Profit and Loss Percentage
- Population Growth Problems
- Depreciation Problems
- Discount Problems
- Consumption Reduction Problems
- Percentage Error Problems
Example 1: Basic Percentage Calculation
Question: Find 25% of 480.
Solution:
25% = 25/100
Required value:
= (25/100) × 480
= 120
Therefore:
25% of 480 = 120
Example 2: Fraction to Percentage Conversion
Question: Convert 3/5 into percentage.
Solution:
Percentage:
= (3/5) × 100
= 60%
Therefore:
3/5 = 60%
Example 3: Percentage to Fraction Conversion
Question: Convert 75% into fraction.
Solution:
75%
= 75/100
= 3/4
Therefore:
75% = 3/4
Example 4: Percentage Increase
Question: A price increases from 400 to 520. Find the percentage increase.
Solution:
Increase:
= 520 − 400
= 120
Percentage increase:
= (120/400) × 100
= 30%
Therefore:
Percentage increase = 30%
Example 5: Percentage Decrease
Question: A value decreases from 900 to 720. Find the percentage decrease.
Solution:
Decrease:
= 900 − 720
= 180
Percentage decrease:
= (180/900) × 100
= 20%
Therefore:
Percentage decrease = 20%
Example 6: Successive Percentage Increase
Question: A quantity increases successively by 20% and 10%. Find the net percentage increase.
Solution:
Net change:
= 20 + 10 + (20 × 10)/100
= 20 + 10 + 2
= 32%
Therefore:
Net increase = 32%
Example 7: Equal Percentage Increase and Decrease
Question: A value increases by 20% and then decreases by 20%. Find the net percentage change.
Solution:
Net decrease:
= (20 × 20)/100
= 4%
Therefore:
Net decrease = 4%
Example 8: Population Growth Problem
Question: The population of a town is 20000. If it increases by 10% annually, find the population after 2 years.
Solution:
Population after n years:
= P(1 + R/100)n
= 20000(1 + 10/100)²
= 20000(1.1)²
= 20000 × 1.21
= 24200
Therefore:
Population after 2 years = 24200
Example 9: Depreciation Problem
Question: The value of a machine is 50000. If it depreciates by 10% annually, find its value after 2 years.
Solution:
Value after depreciation:
= 50000(1 − 10/100)²
= 50000(0.9)²
= 50000 × 0.81
= 40500
Therefore:
Machine value after 2 years = 40500
Example 10: Profit Percentage
Question: A shopkeeper buys an article for 800 and sells it for 1000. Find the profit percentage.
Solution:
Profit:
= 1000 − 800
= 200
Profit percentage:
= (200/800) × 100
= 25%
Therefore:
Profit percentage = 25%
Example 11: Loss Percentage
Question: A trader buys a product for 1200 and sells it for 1020. Find the loss percentage.
Solution:
Loss:
= 1200 − 1020
= 180
Loss percentage:
= (180/1200) × 100
= 15%
Therefore:
Loss percentage = 15%
Example 12: Discount Problem
Question: A shopkeeper gives a 20% discount on an article marked at 2500. Find the selling price.
Solution:
Discount:
= 20% of 2500
= 500
Selling price:
= 2500 − 500
= 2000
Therefore:
Selling price = 2000
Example 13: Reverse Percentage Problem
Question: After a 25% increase, the price of an article becomes 500. Find the original price.
Solution:
Original price:
= 500 × 100/125
= 400
Therefore:
Original price = 400
Example 14: Consumption Reduction Problem
Question: The price of sugar increases by 25%. By what percentage should consumption be reduced to maintain the same expenditure?
Solution:
Required reduction:
= [25/(100 + 25)] × 100
= 25/125 × 100
= 20%
Therefore:
Consumption should be reduced by 20%
Example 15: Percentage Error Problem
Question: A student calculates a value as 96 instead of 80. Find the percentage error.
Solution:
Error:
= 96 − 80
= 16
Percentage error:
= (16/80) × 100
= 20%
Therefore:
Percentage error = 20%
Example 16: Marks Percentage Problem
Question: A student secures 420 marks out of 600. Find the percentage obtained.
Solution:
Percentage:
= (420/600) × 100
= 70%
Therefore:
Percentage obtained = 70%
Example 17: Comparison Percentage Problem
Question: A is 25% more than B. By what percentage is B less than A?
Solution:
Required percentage:
= [25/(100 + 25)] × 100
= 25/125 × 100
= 20%
Therefore:
B is 20% less than A
Example 18: Successive Discount Problem
Question: Two successive discounts of 10% and 20% are given on an article. Find the net discount percentage.
Solution:
Net discount:
= 10 + 20 − (10 × 20)/100
= 30 − 2
= 28%
Therefore:
Net discount = 28%
Important Exam Tips
- Memorize common fraction-percentage conversions.
- Always identify the correct base value.
- Use successive percentage formulas carefully.
- Convert percentages into decimals for quick calculations.
- Practice reverse percentage methods regularly.
- Use approximation techniques in MCQs.
- Verify calculations to avoid percentage errors.
Practicing solved examples regularly improves conceptual clarity, calculation speed, and accuracy in solving Percentage questions in competitive examinations.