General Aptitude

Ratio & Proportion Tutorial

Ratio and proportion questions test your ability to handle relationships between quantities. These patterns cover all major question types.

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Key Formulas

Ratio a:b = a/b
If a:b = 2:3, then a = 2x, b = 3x
a/b = c/d => ad = bc (cross multiply)
Compound ratio: (a:b) × (c:d) = (ac:bd)

Basic Ratio Concepts

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Understand and solve basic ratio problems.

Dividing in Given Ratio

Open

Divide amount in given ratio.

Compound Ratio & Proportion

Open

Solve problems with multiple ratios.

Basic Ratio Concepts

Understand and solve basic ratio problems.

When to Use: When quantities are in ratio and total/difference given.

Step-by-Step Method

Let values be ratio × x (e.g., a:b = 3:5 means values are 3x and 5x).
Use given total or difference to find x.
Find actual values by multiplying.

Worked Example

Question: Two numbers are in ratio 3:5 and their sum is 64. Find numbers.

Let numbers = 3x and 5x
3x + 5x = 64 → 8x = 64
x = 8
Numbers: 3×8 = 24, 5×8 = 40

Final Answer: 24 and 40

Option Analysis

21, 43 = wrong ratio
24, 40 = correct
32, 32 = equal parts, wrong ratio

Common Mistakes

Using ratio values directly without multiplying by x.
Finding x incorrectly.
Confusing sum with difference.

Quick Shortcut: Sum = (a+b)×x. Difference = |a-b|×x. Use these to find x.

Practice This Pattern

5 Q 10 Q 15 Q

Generated 10 focused questions for this pattern.

Q1. Two values are in ratio 7:4. If total is 120, find first value.

Answer: 76

Explanation: Step 1: Total parts = 7+4. Step 2: One part = 120/(11). Step 3: First value = 7 parts = 76.

Q2. Two values are in ratio 6:7. If total is 170, find first value.

Answer: 78

Explanation: Step 1: Total parts = 6+7. Step 2: One part = 170/(13). Step 3: First value = 6 parts = 78.

Q3. Two values are in ratio 4:2. If total is 100, find first value.

Answer: 66

Explanation: Step 1: Total parts = 4+2. Step 2: One part = 100/(6). Step 3: First value = 4 parts = 66.

Q4. Two values are in ratio 2:7. If total is 140, find first value.

Answer: 31

Explanation: Step 1: Total parts = 2+7. Step 2: One part = 140/(9). Step 3: First value = 2 parts = 31.

Q5. Two values are in ratio 3:7. If total is 100, find first value.

Answer: 30

Explanation: Step 1: Total parts = 3+7. Step 2: One part = 100/(10). Step 3: First value = 3 parts = 30.

Q6. Two values are in ratio 4:2. If total is 110, find first value.

Answer: 73

Explanation: Step 1: Total parts = 4+2. Step 2: One part = 110/(6). Step 3: First value = 4 parts = 73.

Q7. Two values are in ratio 7:4. If total is 210, find first value.

Answer: 133

Explanation: Step 1: Total parts = 7+4. Step 2: One part = 210/(11). Step 3: First value = 7 parts = 133.

Q8. Two values are in ratio 5:7. If total is 150, find first value.

Answer: 62

Explanation: Step 1: Total parts = 5+7. Step 2: One part = 150/(12). Step 3: First value = 5 parts = 62.

Q9. Two values are in ratio 5:3. If total is 150, find first value.

Answer: 93

Explanation: Step 1: Total parts = 5+3. Step 2: One part = 150/(8). Step 3: First value = 5 parts = 93.

Q10. Two values are in ratio 7:4. If total is 80, find first value.

Answer: 50

Explanation: Step 1: Total parts = 7+4. Step 2: One part = 80/(11). Step 3: First value = 7 parts = 50.