Percentage of a Quantity

Finding "X% of Y" is the most basic percentage calculation, but it appears in countless QR questions — directly or as part of a multi-step problem. This lesson covers efficient methods for calculating percentages, finding the original amount (reverse percentages), and recognising the common percentage question types.

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Finding X% of Y

Method 1: The Building-Block Method

Break the percentage into components you can calculate instantly:

Component	How to Find It
1%	Divide by 100
5%	Half of 10%
10%	Divide by 10
25%	Divide by 4
50%	Divide by 2

Example: Find 23% of 4,800

• 10% of 4,800 = 480
• 20% = 2 × 480 = 960
• 3% = 3 × 48 = 144
• 23% = 960 + 144 = 1,104

Method 2: The Decimal Multiplier

Convert the percentage to a decimal and multiply:

• 23% of 4,800 = 0.23 × 4,800

This is particularly useful when using the calculator. Enter: 0.23 × 4,800 =

Method 3: The Fraction Method

Convert the percentage to a fraction:

Example: 25% of 360

• 25% = 1/4
• 360 ÷ 4 = 90

This is fastest when the percentage has a simple fractional equivalent.

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Common Percentages and Their Shortcuts

Percentage	Shortcut	Example: % of 840
1%	÷ 100	8.4
5%	÷ 20 or half of 10%	42
10%	÷ 10	84
12.5%	÷ 8	105
20%	÷ 5	168
25%	÷ 4	210
33.3%	÷ 3	280
50%	÷ 2	420
75%	÷ 4 × 3	630

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Finding the Original Amount (Reverse Percentages)

When you know the result of a percentage calculation and need to find the original amount.

After an Increase

"After a 15% increase, the price is £460. What was the original price?"

• £460 represents 115% of the original (100% + 15%)
• Original = £460 ÷ 1.15 = £400

After a Decrease

"After a 20% discount, a laptop costs £680. What was the original price?"

• £680 represents 80% of the original (100% − 20%)
• Original = £680 ÷ 0.80 = £850

The Common Mistake

Wrong: "The price after a 20% increase is £600. Original = £600 − 20% of £600 = £600 − £120 = £480."

Right: Original = £600 ÷ 1.20 = £500

Check: £500 × 1.20 = £600 ✓. But £480 × 1.20 = £576 ≠ £600 ✗

The mistake is subtracting 20% of the new value instead of dividing by 1.20. The 20% increase was applied to the original, not the new value.

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