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Percentage Simplification

Introduction

Percentage simplification problems test how quickly you can calculate with percentages. These are common in exams - especially in profit and loss, discounts, data interpretation, and ratio problems. Converting percentages into fractions or decimals makes calculations fast and accurate.

Pattern: Percentage Simplification

Pattern

Key idea: Convert % into fraction or decimal (x% = x/100), then multiply or divide to simplify step by step.

Step-by-Step Example

Question

Find 25% of 240.

Options:

  • A) 40
  • B) 50
  • C) 60
  • D) 75

Solution

  1. Step 1: Convert percentage to fraction

    25% = 25/100 = 1/4.

  2. Step 2: Multiply with the given number

    (1/4) × 240 = 240 ÷ 4.

  3. Step 3: Simplify the result

    240 ÷ 4 = 60.

  4. Final Answer:

    60 → Option C.

  5. Quick Check:

    10% of 240 = 24, so 25% = 2.5 × 24 = 60 ✅

Quick Variations

1. x% of y → (x/100) × y.

2. Increase by p% → New value = Original × (1 + p/100).

3. Decrease by p% → New value = Original × (1 - p/100).

4. Use fractions for common percentages: 50% = 1/2, 25% = 1/4, 20% = 1/5, 12.5% = 1/8.

Trick to Always Use

  • Step 1 → Convert % into easy fractions whenever possible.
  • Step 2 → Use 10% and 1% as building blocks for quick estimates.
  • Step 3 → For increases/decreases, directly multiply by (1 ± p/100).

Summary

Summary

  • Convert % to fractions or decimals first.
  • Use common % values (10%, 25%, 50%) for faster mental math.
  • Apply (1 + p/100) or (1 - p/100) for direct percentage increase/decrease.
  • Always verify with a quick 10% or 1% estimation.

Example to remember:
25% of 240 = 60

Practice

(1/5)
1. Find 20% of 250.
easy
A. 50
B. 55
C. 45
D. 60

Solution

  1. Step 1: Convert percent to fraction

    Convert percent to fraction: 20% = 20/100 = 1/5.

  2. Step 2: Multiply with the number

    (1/5) × 250 = 250 ÷ 5 = 50.

  3. Final Answer:

    50 → Option A.

  4. Quick Check:

    10% of 250 = 25, so 20% = 2 × 25 = 50 ✅
Hint: Convert 20% to 1/5 for fast division.
Common Mistakes: Multiplying 250 × 20 and forgetting to divide by 100.
2. Find 12.5% of 64.
easy
A. 6
B. 8
C. 10
D. 12

Solution

  1. Step 1: Recognise the fraction form

    Recognize 12.5% = 1/8.

  2. Step 2: Multiply with the number

    (1/8) × 64 = 64 ÷ 8 = 8.

  3. Final Answer:

    8 → Option B.

  4. Quick Check:

    Half of 64 = 32, half again = 16, half again = 8 ✅
Hint: Remember 12.5% = 1/8 for quick division.
Common Mistakes: Using 12.5/100 directly without recognizing the fraction shortcut.
3. A number is increased by 10%. If the original number is 150, what is the new value?
easy
A. 160
B. 162
C. 165
D. 170

Solution

  1. Step 1: Set up the multiplier for increase

    Increase by 10% → multiply by (1 + 10/100) = 1.1.

  2. Step 2: Multiply

    150 × 1.1 = 165.

  3. Final Answer:

    165 → Option C.

  4. Quick Check:

    10% of 150 = 15; 150 + 15 = 165 ✅
Hint: For a p% increase, multiply by (1 + p/100).
Common Mistakes: Adding p instead of p% of the number.
4. Find 40% of 360 - 25% of 200.
medium
A. 64
B. 66
C. 68
D. 94

Solution

  1. Step 1: Compute 40% of 360

    40% of 360 = (40/100) × 360 = 0.4 × 360 = 144.

  2. Step 2: Compute 25% of 200

    25% of 200 = (25/100) × 200 = 0.25 × 200 = 50.

  3. Step 3: Subtract the results

    144 - 50 = 94.

  4. Final Answer:

    94 → Option D.

  5. Quick Check:

    40% of 360 is 144 (10% = 36), 25% of 200 is 50, 144 - 50 = 94 ✅
Hint: Compute each percent separately, then combine with +/- as needed.
Common Mistakes: Applying the percentage to the wrong number or forgetting to subtract after computing both parts.
5. The price of an item is decreased by 20%. If the original price was 250, what is the new price?
medium
A. 200
B. 195
C. 190
D. 210

Solution

  1. Step 1: Set up the multiplier for decrease

    Decrease by 20% → multiply by (1 - 20/100) = 0.8.

  2. Step 2: Multiply

    250 × 0.8 = 200.

  3. Final Answer:

    200 → Option A.

  4. Quick Check:

    20% of 250 = 50; 250 - 50 = 200 ✅
Hint: For p% decrease, multiply by (1 - p/100) to get the new value directly.
Common Mistakes: Subtracting p instead of p% of the original value.

Mock Test

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