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Percentage Comparison

Introduction

कई aptitude questions में आपको ऐसे statements मिलेंगे जैसे A is x% more than B या A is x% less than B।

ये questions आपकी relative comparison समझ को test करते हैं। मुख्य बात है: base value को सही पहचानकर sentence को math में बदलना।

Pattern: Percentage Comparison

Pattern

अगर A, B से x% अधिक है → A = B × (1 + x/100)

अगर A, B से x% कम है → A = B × (1 - x/100)

Reverse relation: अगर A, B से x% अधिक है → B, A से (x / (100 + x)) × 100 % कम है।

Step-by-Step Example

Question

अगर A की salary, B की salary से 25% अधिक है, और B की salary ₹40,000 है, तो A की salary निकालें। साथ ही यह भी बताएं कि B की salary, A से कितने प्रतिशत कम है।

Solution

  1. Step 1: B की salary लिखें।

    Sentence: B’s salary = 40,000.

  2. Step 2: A की salary लिखें (more than case)।

    Sentence: A is 25% more than B → A = B × (1 + 25/100).
    Math: A = 40,000 × 1.25 = 50,000

  3. Step 3: Reverse comparison निकालें।

    Sentence: B is how much % less than A?
    Difference = A - B = 50,000 - 40,000 = 10,000
    Percentage less = (Difference ÷ A) × 100
    Math: (10,000 ÷ 50,000) × 100 = 20%

  4. Step 4: Final Answer.

    A की salary = ₹50,000
    B की salary, A से 20% कम है

  5. Step 5: Quick Check.

    40,000 का 25% = 10,000 → 40,000 + 10,000 = 50,000 ✅
    10,000, 50,000 का 20% है ✅

Quick Variations

अगर A, B से 40% अधिक है: A = 1.4B, और B = (40/140) × 100 = 28.57% कम है A से।

अगर A, B से 30% कम है: A = 0.7B, और B = (30/70) × 100 = 42.86% अधिक है A से।

Trick to Always Use

  • Step 1: “More than” → (1 + x/100) से multiply करें।
  • Step 2: “Less than” → (1 - x/100) से multiply करें।
  • Step 3: Reverse relation के लिए difference को बड़े base से compare करें।
  • Step 4: Direct subtraction से हमेशा cross-check करें।

Summary

Summary

Percentage Comparison pattern का पूरा खेल सही base चुनने का है।

  • A, B से अधिक है: A = B × (1 + x/100).
  • A, B से कम है: A = B × (1 - x/100).
  • Reverse relation: Base बड़े value पर shift होता है।

ध्यान रखें: “more than” और “less than” हमेशा relative होते हैं। Base value सही चुनें।

Practice

(1/5)
1. If A is 20% more than B and B = 100, what is the value of A?
easy
A. 110
B. 115
C. 120
D. 125

Solution

  1. Step 1: Write relation.

    A = B × (1 + 20/100).

  2. Step 2: Substitute B = 100.

    A = 100 × 1.20 = 120.

  3. Step 3: Final Answer.

    A = 120.

  4. Quick Check.

    20% of 100 = 20 → 100 + 20 = 120 ✅
Hint: For x% more, multiply by (1 + x/100).
Common Mistakes: Adding 20 instead of 20% of the base.
2. If A is 25% less than B and B = 80, what is the value of A?
easy
A. 55
B. 60
C. 65
D. 70

Solution

  1. Step 1: Write relation.

    A = B × (1 - 25/100).

  2. Step 2: Substitute B = 80.

    A = 80 × 0.75 = 60.

  3. Step 3: Final Answer.

    A = 60.

  4. Quick Check.

    25% of 80 = 20 → 80 - 20 = 60 ✅
Hint: For x% less, multiply by (1 - x/100).
Common Mistakes: Subtracting 25 directly instead of 25% of the base.
3. A is 30% more than B. If A = 130, find B.
medium
A. 90
B. 95
C. 100
D. 105

Solution

  1. Step 1: Write relation.

    A = B × 1.30.

  2. Step 2: Substitute A = 130.

    130 = B × 1.30 → B = 130 ÷ 1.30 = 100.

  3. Step 3: Final Answer.

    B = 100.

  4. Quick Check.

    100 × 1.30 = 130 ✅
Hint: Divide A by (1 + x/100) to get B.
Common Mistakes: Subtracting 30 directly instead of percentage-based relation.
4. B is 40% less than A. If B = 90, find A.
medium
A. 140
B. 145
C. 150
D. 155

Solution

  1. Step 1: Write relation.

    B = A × 0.60.

  2. Step 2: Substitute B = 90.

    90 = A × 0.60 → A = 90 ÷ 0.60 = 150.

  3. Step 3: Final Answer.

    A = 150.

  4. Quick Check.

    40% of 150 = 60 → 150 - 60 = 90 ✅
Hint: Divide the smaller by (1 - x/100) to find the bigger.
Common Mistakes: Adding 40 instead of reversing the percentage relation.
5. A is 50% more than B. By what percent is B less than A?
medium
A. 33.33%
B. 40%
C. 50%
D. 25%

Solution

  1. Step 1: Assume B = 100.

    A = 100 × 1.50 = 150.

  2. Step 2: Find difference.

    A - B = 150 - 100 = 50.

  3. Step 3: Express as percent of A.

    50 ÷ 150 × 100 = 33.33%.

  4. Step 4: Final Answer.

    B is 33.33% less than A.

  5. Quick Check.

    100 is 33.33% less than 150 ✅
Hint: Reverse % relation uses larger value as base.
Common Mistakes: Taking percent of B instead of A when reversing relation.

Mock Test

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