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Percentage of a Quantity

Introduction

A very common type of percentage question is finding a percentage of a number. These problems appear often in exams and daily life - like calculating discounts, tax, or marks.

The method is simple: multiply the number by the percentage (written as a fraction or decimal).

Pattern: Percentage of a Quantity

Pattern

The key idea: To find x% of a number y → (x/100) × y.

Convert the percentage into fraction or decimal, multiply with the given quantity, and simplify.

Step-by-Step Example

Question

Find 25% of 480.

Solution

  1. Step 1: Write the formula

    Sentence: To find percentage of a number, multiply (percentage ÷ 100) with the number.
    Math: (x% of y) = (x/100) × y

  2. Step 2: Substitute values

    Sentence: We need 25% of 480.
    Math: (25/100) × 480

  3. Step 3: Simplify the fraction

    25/100 = 1/4
    (1/4) × 480 = 120

  4. Final Answer:

    120

  5. Quick Check:

    10% of 480 = 48 → 20% = 96 → add 5% (24) → 96 + 24 = 120 ✅

Quick Variations

50% of a number = half the number.

25% of a number = one-fourth of the number.

10% of a number = one-tenth of the number.

Using these shortcuts can save a lot of time in exams.

Trick to Always Use

  • Step 1: Convert % into fraction/decimal.
  • Step 2: Multiply by the given number.
  • Step 3: Simplify quickly using mental math if possible.
  • Step 4: Verify with an alternate breakdown (like 10% + 5%).

Summary

Summary

  • Use the formula (x% of y) = (x/100) × y to find percentage of a quantity.
  • Convert the percentage into a simple fraction or decimal before multiplying.
  • Simplify the multiplication (use fraction shortcuts like 25% = 1/4, 12.5% = 1/8).
  • Always perform a quick check by breaking the percentage into easy parts (e.g., 10% + 5%).

Example to remember:
25% of 480 = 120

Practice

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

Solution

  1. Step 1: Apply the percentage formula

    To find x% of y → (x/100) × y.

  2. Step 2: Substitute the values

    (20/100) × 250 = 0.2 × 250 = 50.

  3. Final Answer:

    50 → Option A

  4. Quick Check:

    10% of 250 = 25 → double it = 50 ✅
Hint: 10% = 25 → 20% = 2 × 25 = 50.
Common Mistakes: Dividing by 20 instead of multiplying by 20%.
2. Find 15% of 480.
easy
A. 70
B. 72
C. 75
D. 80

Solution

  1. Step 1: Use the percentage formula

    (15% of 480) = (15/100) × 480.

  2. Step 2: Perform the calculation

    (15/100) × 480 = 72.

  3. Final Answer:

    72 → Option B

  4. Quick Check:

    10% of 480 = 48, 5% = 24 → 48+24 = 72 ✅
Hint: Break 15% into 10% + 5%.
Common Mistakes: Using 480 ÷ 15 instead of ×15%.
3. A student spends 30% of his 2000 rupees allowance on books. How much did he spend?
easy
A. 500
B. 600
C. 650
D. 550

Solution

  1. Step 1: Form the percentage expression

    Spent = 30% of 2000.

  2. Step 2: Calculate the value

    (30/100) × 2000 = 600.

  3. Final Answer:

    600 → Option B

  4. Quick Check:

    10% of 2000 = 200 → 3 × 200 = 600 ✅
Hint: 30% = 3 × 10%. Find 10% first then triple it.
Common Mistakes: Multiplying 2000 × 30 instead of ×30/100.
4. What is 12.5% of 96?
medium
A. 10
B. 11
C. 12
D. 12.5

Solution

  1. Step 1: Convert the percentage to fraction

    12.5% = 12.5/100 = 1/8.

  2. Step 2: Multiply with the number

    (1/8) × 96 = 12.

  3. Final Answer:

    12 → Option C

  4. Quick Check:

    8 × 12 = 96 → 1/8 of 96 = 12 ✅
Hint: Remember 12.5% = 1/8.
Common Mistakes: Treating 12.5% as 0.12 instead of 0.125.
5. Find 8% of 625.
medium
A. 48
B. 49
C. 50
D. 52

Solution

  1. Step 1: Convert % into usable form

    (8% of 625) = (8/100) × 625.

  2. Step 2: Compute using 1% method

    625 ÷ 100 = 6.25 → 6.25 × 8 = 50.

  3. Final Answer:

    50 → Option C

  4. Quick Check:

    1% of 625 = 6.25 → 8% = 8×6.25 = 50 ✅
Hint: Find 1% first then multiply by 8.
Common Mistakes: Multiplying 625 × 8 without dividing by 100.

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