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Percentage Comparison

Introduction

In many aptitude questions, you’ll see statements like A is x% more than B or A is x% less than B.

These problems test your understanding of relative comparison. The key is to carefully translate the sentence into math without mixing up the base value.

Pattern: Percentage Comparison

Pattern

If A is x% more than B → A = B × (1 + x/100)

If A is x% less than B → A = B × (1 - x/100)

Reverse relation: If A is x% more than B → B is (x / (100 + x)) × 100 % less than A.

Step-by-Step Example

Question

If A’s salary is 25% more than B’s salary, and B’s salary is ₹40,000, find A’s salary. Also find how much percent B’s salary is less than A’s.

Solution

  1. Step 1: Represent B’s salary.

    Sentence: B’s salary = 40,000.

  2. Step 2: Write A’s salary (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: Find reverse comparison.

    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’s salary = ₹50,000
    B’s salary is 20% less than A’s

  5. Step 5: Quick Check.

    25% of 40,000 = 10,000 → 40,000 + 10,000 = 50,000 ✅
    10,000 is 20% of 50,000 ✅

Quick Variations

If A is 40% more than B: A = 1.4B, and B is (40/140) × 100 = 28.57% less than A.

If A is 30% less than B: A = 0.7B, and B is (30/70) × 100 = 42.86% more than A.

Trick to Always Use

  • Step 1: “More than” → Multiply by (1 + x/100).
  • Step 2: “Less than” → Multiply by (1 - x/100).
  • Step 3: For reverse relation, compare difference with the larger base.
  • Step 4: Always double-check with direct subtraction.

Summary

Summary

The Percentage Comparison pattern works by choosing the correct base value.

  • A more than B: A = B × (1 + x/100).
  • A less than B: A = B × (1 - x/100).
  • Reverse relation: Base shifts to the larger value.

Be careful: “more than” and “less than” are relative. Always check which number is the base.

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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