🚫 Percentage - Common Mistakes to Avoid

Master percentage calculations by understanding and avoiding these common pitfalls that cost marks in IBPS exams.

🔍 Most Common Mistakes

1. Basic Percentage Calculation Errors

Mistake: Not converting percentage to fraction/decimal

Problem: Find 25% of 80.

❌ Wrong Approach:
25% of 80 = 25 × 80 = 2,000

✓ Correct Approach:
25% of 80 = (25/100) × 80 = (1/4) × 80 = 20

Practice Question:

Find 18% of 450.

Solution:

• 18% of 450 = (18/100) × 450 = 0.18 × 450 = 81

2. Percentage Increase/Decrease Errors

Mistake: Using wrong base for calculation

Problem: Price increases from ₹80 to ₹100. Find percentage increase.

❌ Wrong Approach:
(100/80) × 100 = 125%

✓ Correct Approach:
[(100-80)/80] × 100 = (20/80) × 100 = 25%

Practice Question:

Salary decreases from ₹12,000 to ₹10,200. Find percentage decrease.

Solution:

• Decrease = 12,000 - 10,200 = ₹1,800
• Percentage decrease = (1,800/12,000) × 100 = 15%

3. Successive Percentage Changes

Mistake: Adding or subtracting percentages directly

Problem: Price increases by 20% and then decreases by 10%.

❌ Wrong Approach:
Net change = 20% - 10% = 10% increase

✓ Correct Approach:
Let original price = ₹100
After 20% increase = 100 × 1.2 = ₹120
After 10% decrease = 120 × 0.9 = ₹108
Net change = 8% increase

Formula: Net change = a + b + (a × b)/100
= 20 + (-10) + (20 × -10)/100 = 20 - 10 - 2 = 8%

Practice Question:

A number increases by 30% and then decreases by 20%. Find net percentage change.

Solution:

• Using formula: Net change = 30 + (-20) + (30 × -20)/100 = 30 - 20 - 6 = 4%
• Net increase = 4%

4. Population Growth and Depreciation

Mistake: Using simple interest instead of compound growth

Problem: Population is 50,000, grows at 5% annually. Find after 3 years.

❌ Wrong Approach:
Population = 50,000 + (50,000 × 5 × 3)/100 = 57,500

✓ Correct Approach:
Population = 50,000 × (1.05)³ = 50,000 × 1.157625 = 57,881.25

Practice Question:

A machine worth ₹20,000 depreciates at 10% per annum. Find its value after 2 years.

Solution:

• Value after 2 years = 20,000 × (0.9)² = 20,000 × 0.81 = ₹16,200

5. Election and Voting Problems

Mistake: Not accounting for invalid votes properly

Problem: 8,000 voters, 20% invalid votes. Winner got 60% of valid votes.

❌ Wrong Approach:
Winner's votes = 8,000 × 60% = 4,800

✓ Correct Approach:
Valid votes = 8,000 × 80% = 6,400
Winner's votes = 6,400 × 60% = 3,840

Practice Question:

In an election, 15,000 votes were polled. 10% were invalid. The winner got 55% of valid votes and won by 1,200 votes. Find the loser’s votes.

Solution:

• Valid votes = 15,000 × 90% = 13,500
• Winner’s votes = 13,500 × 55% = 7,425
• Loser’s votes = 7,425 - 1,200 = 6,225

6. Fraction to Percentage Conversion

Mistake: Incorrect conversion methods

Problem: Convert 3/8 to percentage.

❌ Wrong Approach:
3/8 = 3.8%

✓ Correct Approach:
3/8 × 100 = (3 × 100)/8 = 300/8 = 37.5%

Practice Question:

Convert 7/20 to percentage.

Solution:

• 7/20 × 100 = 35%

7. Percentage in Profit and Loss

Mistake: Wrong base for percentage calculation

Problem: Cost Price = ₹200, Selling Price = ₹250. Find profit percentage.

❌ Wrong Approach:
Profit % = (50/250) × 100 = 20%

✓ Correct Approach:
Profit % = (50/200) × 100 = 25%

Practice Question:

A shopkeeper sells an article for ₹720 at a loss of 10%. Find the cost price.

Solution:

• Let CP = x
• SP = x × (100-10)/100 = 0.9x
• 0.9x = 720
• x = 720/0.9 = ₹800

8. Percentage Error in Data Interpretation

Mistake: Wrong identification of base value

Problem: Sales in 2020 = ₹200 lakhs, Sales in 2021 = ₹250 lakhs.
Find percentage increase in 2021 compared to 2020.

❌ Wrong Approach:
(250/200) × 100 = 125%

✓ Correct Approach:
[(250-200)/200] × 100 = (50/200) × 100 = 25%

Practice Question:

A company’s expenses were ₹80,000 in 2020 and ₹96,000 in 2021. By what percentage did expenses increase?

Solution:

• Increase = 96,000 - 80,000 = ₹16,000
• Percentage increase = (16,000/80,000) × 100 = 20%

9. Mixed Percentage Problems

Mistake: Not understanding weighted averages

Problem: A student scored 75% in Maths (weight 40%) and 85% in other subjects.
Find overall percentage.

❌ Wrong Approach:
Average = (75 + 85)/2 = 80%

✓ Correct Approach:
Overall % = (75 × 40% + 85 × 60%) = 30 + 51 = 81%

Practice Question:

A product contains 30% of ingredient A and 70% of ingredient B. Ingredient A has 20% fat and B has 5% fat. Find total fat percentage.

Solution:

• Fat from A = 30% × 20% = 6%
• Fat from B = 70% × 5% = 3.5%
• Total fat = 6% + 3.5% = 9.5%

10. Complex Multi-step Problems

Mistake: Missing intermediate steps

Problem: A number is first increased by 25%, then decreased by 20%.
If final value is 240, find original number.

❌ Wrong Approach:
Working backwards incorrectly

✓ Correct Approach:
Let original = x
After 25% increase = x × 1.25
After 20% decrease = x × 1.25 × 0.8 = x × 1.0
x × 1.0 = 240
Therefore, x = 240

Practice Question:

After two successive discounts of 20% and 10%, an article costs ₹432. Find the marked price.

Solution:

• Let MP = x
• After 20% discount = x × 0.8
• After 10% discount = x × 0.8 × 0.9 = x × 0.72
• x × 0.72 = 432
• x = 432/0.72 = ₹600

🎯 Special Cases and Advanced Mistakes

11. Percentage Point vs Percentage Change

Mistake: Confusing absolute and relative change

Problem: Interest rate increases from 8% to 12%.

❌ Wrong Approach:
Saying "interest increased by 4%" (this is percentage points)

✓ Correct Approach:
Percentage increase = (12-8)/8 × 100 = 50%
Percentage points = 12% - 8% = 4 percentage points

12. Ratio and Percentage Combination

Mistake: Not maintaining consistent base

Problem: A:B = 3:2. B is 40% more than C. If C = 300, find A.

❌ Wrong Approach:
B = 300 × 40% = 120

✓ Correct Approach:
B = 300 × 140% = 420
A = (3/2) × 420 = 630

📝 Practice Questions to Avoid Mistakes

Set 1: Basic Calculations

1. Find 35% of 280
2. What percent is 45 of 150?
3. Find 12.5% of 640

Set 2: Increase/Decrease

4. Price increases from 75 to 90. Find % increase
5. Population decreases from 80,000 to 68,000. Find % decrease
6. Salary increases by 15% and becomes ₹23,000. Find original salary

Set 3: Successive Changes

7. 20% increase followed by 10% increase
8. 30% increase followed by 20% decrease
9. 10% decrease followed by 15% increase

Set 4: Complex Problems

10. After 25% discount and 5% tax, item costs ₹2,375. Find list price
11. A student needs 40% to pass. Scores 35% in first paper (weight 60%) and 50% in second. Does he pass?
12. Election: 10,000 voters, 20% invalid, winner got 55% of valid votes and won by 800 votes. Find loser’s votes

🎯 Quick Tips to Avoid Mistakes

Calculation Tips:

1. Always identify the base - What represents 100%?
2. Convert percentage to decimal - 25% = 0.25
3. Use fraction equivalents - 25% = 1/4, 20% = 1/5
4. Write formula first - Before substituting values

Verification Tips:

1. Estimate answer - Should it be more or less than 50%?
2. Check reasonableness - 90% of 100 should be 90, not 900
3. Reverse calculate - If 25% of 80 = 20, then 20/80 should = 25%

Common Conversions to Remember:

• 1% = 1/100, 5% = 1/20, 10% = 1/10
• 12.5% = 1/8, 20% = 1/5, 25% = 1/4
• 33.33% = 1/3, 50% = 1/2, 75% = 3/4

🔗 Related Topics

📚 Quick Formula Reference

• X% of Y: (X/100) × Y
• Percentage Increase: [(New-Old)/Old] × 100
• Percentage Decrease: [(Old-New)/Old] × 100
• Successive % Change: a + b + (a × b)/100
• Population Growth: P × (1 + r/100)ⁿ
• Depreciation: P × (1 - r/100)ⁿ

Remember: Percentage means per hundred - always think about what the whole (100%) represents in each problem.