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

Basic Ratio Concepts

Open

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

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

Worked Example

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

  1. Let numbers = 3x and 5x
  2. 3x + 5x = 64 → 8x = 64
  3. x = 8
  4. Numbers: 3×8 = 24, 5×8 = 40

Final Answer: 24 and 40

Option Analysis

Common Mistakes

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 15 focused questions for this pattern.

Q1. Two values are in ratio 2:2. If total is 180, find first value.

  • 90
  • 87
  • 93
  • 96

Answer: 90

Explanation: Step 1: Total parts = 2+2. Step 2: One part = 180/(4). Step 3: First value = 2 parts = 90.

Q2. Two values are in ratio 3:3. If total is 220, find first value.

  • 110
  • 116
  • 107
  • 113

Answer: 110

Explanation: Step 1: Total parts = 3+3. Step 2: One part = 220/(6). Step 3: First value = 3 parts = 110.

Q3. Two values are in ratio 5:2. If total is 170, find first value.

  • 124
  • 127
  • 121
  • 118

Answer: 121

Explanation: Step 1: Total parts = 5+2. Step 2: One part = 170/(7). Step 3: First value = 5 parts = 121.

Q4. Two values are in ratio 4:4. If total is 120, find first value.

  • 66
  • 60
  • 63
  • 57

Answer: 60

Explanation: Step 1: Total parts = 4+4. Step 2: One part = 120/(8). Step 3: First value = 4 parts = 60.

Q5. Two values are in ratio 3:7. If total is 90, find first value.

  • 30
  • 27
  • 24
  • 33

Answer: 27

Explanation: Step 1: Total parts = 3+7. Step 2: One part = 90/(10). Step 3: First value = 3 parts = 27.

Q6. Two values are in ratio 6:5. If total is 180, find first value.

  • 104
  • 98
  • 101
  • 95

Answer: 98

Explanation: Step 1: Total parts = 6+5. Step 2: One part = 180/(11). Step 3: First value = 6 parts = 98.

Q7. Two values are in ratio 7:4. If total is 170, find first value.

  • 114
  • 111
  • 108
  • 105

Answer: 108

Explanation: Step 1: Total parts = 7+4. Step 2: One part = 170/(11). Step 3: First value = 7 parts = 108.

Q8. Two values are in ratio 6:4. If total is 180, find first value.

  • 111
  • 105
  • 114
  • 108

Answer: 108

Explanation: Step 1: Total parts = 6+4. Step 2: One part = 180/(10). Step 3: First value = 6 parts = 108.

Q9. Two values are in ratio 4:5. If total is 140, find first value.

  • 59
  • 68
  • 65
  • 62

Answer: 62

Explanation: Step 1: Total parts = 4+5. Step 2: One part = 140/(9). Step 3: First value = 4 parts = 62.

Q10. Two values are in ratio 4:7. If total is 150, find first value.

  • 60
  • 51
  • 54
  • 57

Answer: 54

Explanation: Step 1: Total parts = 4+7. Step 2: One part = 150/(11). Step 3: First value = 4 parts = 54.

Q11. Two values are in ratio 5:3. If total is 100, find first value.

  • 65
  • 59
  • 68
  • 62

Answer: 62

Explanation: Step 1: Total parts = 5+3. Step 2: One part = 100/(8). Step 3: First value = 5 parts = 62.

Q12. Two values are in ratio 6:6. If total is 90, find first value.

  • 42
  • 51
  • 48
  • 45

Answer: 45

Explanation: Step 1: Total parts = 6+6. Step 2: One part = 90/(12). Step 3: First value = 6 parts = 45.

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

  • 97
  • 106
  • 100
  • 103

Answer: 100

Explanation: Step 1: Total parts = 7+7. Step 2: One part = 200/(14). Step 3: First value = 7 parts = 100.

Q14. Two values are in ratio 6:4. If total is 150, find first value.

  • 90
  • 96
  • 87
  • 93

Answer: 90

Explanation: Step 1: Total parts = 6+4. Step 2: One part = 150/(10). Step 3: First value = 6 parts = 90.

Q15. Two values are in ratio 4:6. If total is 200, find first value.

  • 86
  • 80
  • 77
  • 83

Answer: 80

Explanation: Step 1: Total parts = 4+6. Step 2: One part = 200/(10). Step 3: First value = 4 parts = 80.