General Aptitude

Percentages Tutorial

Master percentages for placement exams. These patterns cover most frequently asked question types. Practice each pattern until you can solve in under 20 seconds.

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Key Formulas

Percent = (Value / Total) × 100
New Value = Old × (100 ± Percent) / 100
Discount = Marked Price - Selling Price
Profit = SP - CP | Profit % = (Profit / CP) × 100
Loss = CP - SP | Loss % = (Loss / CP) × 100

Direct Percentage Calculation

Open

Find percentage of a given number directly.

Percentage Increase/Decrease

Open

Calculate new value after percentage change.

Find Original from New Value

Open

Find base/original value when final value after change is given.

Discount & Markup Problems

Open

Solve marked price, discount, and selling price problems.

Direct Percentage Calculation

Find percentage of a given number directly.

When to Use: When question asks 'what is X% of Y?'

Step-by-Step Method

Identify the percentage value (X%) and base number (Y).
Convert percentage to decimal: X% = X/100.
Multiply: (X/100) × Y.
Simplify step-by-step: divide Y by 100 first, then multiply by X.

Worked Example

Question: What is 25% of 640?

25% = 25/100 = 1/4
Divide 640 by 4 = 160
Or: 640 ÷ 100 = 6.4, then 6.4 × 25 = 160

Final Answer: 160

Option Analysis

64 = 640 ÷ 10 (wrong: used 10% not 25%)
80 = 640 ÷ 8 (wrong method)
160 is correct: 25% = 1/4 of 640

Common Mistakes

Using percentage as whole number without dividing by 100.
Multiplying instead of dividing for common percentages.
Rounding decimals too early.

Quick Shortcut: 25%=1/4, 50%=1/2, 20%=1/5, 10%=1/10. Use these fractions first!

Practice This Pattern

5 Q 10 Q 15 Q

Generated 15 focused questions for this pattern.

Q1. Two values are in ratio 4:5. If total is 220, find first value.

Answer: 97

Explanation: Step 1: Total parts = 4+5. Step 2: One part = 220/(9). Step 3: First value = 4 parts = 97.

Q2. Two values are in ratio 2:4. If total is 190, find first value.

Answer: 63

Explanation: Step 1: Total parts = 2+4. Step 2: One part = 190/(6). Step 3: First value = 2 parts = 63.

Q3. Two values are in ratio 7:2. If total is 120, find first value.

Answer: 93

Explanation: Step 1: Total parts = 7+2. Step 2: One part = 120/(9). Step 3: First value = 7 parts = 93.

Q4. Two values are in ratio 2:2. If total is 130, find first value.

Answer: 65

Explanation: Step 1: Total parts = 2+2. Step 2: One part = 130/(4). Step 3: First value = 2 parts = 65.

Q5. Two values are in ratio 2:5. If total is 140, find first value.

Answer: 40

Explanation: Step 1: Total parts = 2+5. Step 2: One part = 140/(7). Step 3: First value = 2 parts = 40.

Q6. Two values are in ratio 5:4. If total is 140, find first value.

Answer: 77

Explanation: Step 1: Total parts = 5+4. Step 2: One part = 140/(9). Step 3: First value = 5 parts = 77.

Q7. Two values are in ratio 2:5. If total is 130, find first value.

Answer: 37

Explanation: Step 1: Total parts = 2+5. Step 2: One part = 130/(7). Step 3: First value = 2 parts = 37.

Q8. Two values are in ratio 6:3. If total is 210, find first value.

Answer: 140

Explanation: Step 1: Total parts = 6+3. Step 2: One part = 210/(9). Step 3: First value = 6 parts = 140.

Q9. Two values are in ratio 3:6. If total is 80, find first value.

Answer: 26

Explanation: Step 1: Total parts = 3+6. Step 2: One part = 80/(9). Step 3: First value = 3 parts = 26.

Q10. Two values are in ratio 6:3. If total is 80, find first value.

Answer: 53

Explanation: Step 1: Total parts = 6+3. Step 2: One part = 80/(9). Step 3: First value = 6 parts = 53.

Q11. Two values are in ratio 4:7. If total is 190, find first value.

Answer: 69

Explanation: Step 1: Total parts = 4+7. Step 2: One part = 190/(11). Step 3: First value = 4 parts = 69.

Q12. Two values are in ratio 7:2. If total is 220, find first value.

Answer: 171

Explanation: Step 1: Total parts = 7+2. Step 2: One part = 220/(9). Step 3: First value = 7 parts = 171.

Q13. Two values are in ratio 7:6. If total is 200, find first value.

Answer: 107

Explanation: Step 1: Total parts = 7+6. Step 2: One part = 200/(13). Step 3: First value = 7 parts = 107.

Q14. Two values are in ratio 7:5. If total is 110, find first value.

Answer: 64

Explanation: Step 1: Total parts = 7+5. Step 2: One part = 110/(12). Step 3: First value = 7 parts = 64.

Q15. Two values are in ratio 5:6. If total is 120, find first value.

Answer: 54

Explanation: Step 1: Total parts = 5+6. Step 2: One part = 120/(11). Step 3: First value = 5 parts = 54.