Percentage Increase & Decrease — The Ratio Method

This is the single most powerful technique for percentage calculations in exams. Instead of computing percentages the classical way, convert the percentage to a fraction, build the Initial:Final (I:F) ratio, and multiply.

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The Core Idea

When a number changes by a percentage, the Initial and Final values form a simple ratio.

Increase by 20%

• 20% = 1/5
• If Initial = 100, New = 120
• I : F = 5 : 6 (base is 5, add 1)
• So: F = I × 6/5

Increase by 50%

• 50% = 1/2
• I : F = 2 : 3 (base is 2, add 1)
• So: F = I × 3/2

Increase by 37.5%

• 37.5% = 3/8
• I : F = 8 : 11 (base is 8, add 3)
• So: F = I × 11/8

Increase by 36.36%

• 36.36% = 4/11
• I : F = 11 : 15 (base is 11, add 4)
• So: F = I × 15/11

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The Rule

For a percentage = n/d (where d is the base):

• Increase by n/d → I : F = d : (d+n) → F = I × (d+n)/d
• Decrease by n/d → I : F = d : (d−n) → F = I × (d−n)/d

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Complete I:F Ratio Table

Increase (+)

% Change	Fraction	I : F	Multiplier
+6.25%	1/16	16 : 17	× 17/16
+6.67%	1/15	15 : 16	× 16/15
+9.09%	1/11	11 : 12	× 12/11
+10%	1/10	10 : 11	× 11/10
+11.11%	1/9	9 : 10	× 10/9
+12.5%	1/8	8 : 9	× 9/8
+14.28%	1/7	7 : 8	× 8/7
+16.67%	1/6	6 : 7	× 7/6
+20%	1/5	5 : 6	× 6/5
+25%	1/4	4 : 5	× 5/4
+28.56%	2/7	7 : 9	× 9/7
+33.33%	1/3	3 : 4	× 4/3
+50%	1/2	2 : 3	× 3/2

Decrease (−)

% Change	Fraction	I : F	Multiplier
−6.25%	1/16	16 : 15	× 15/16
−6.67%	1/15	15 : 14	× 14/15
−9.09%	1/11	11 : 10	× 10/11
−10%	1/10	10 : 9	× 9/10
−11.11%	1/9	9 : 8	× 8/9
−12.5%	1/8	8 : 7	× 7/8
−14.28%	1/7	7 : 6	× 6/7
−16.67%	1/6	6 : 5	× 5/6
−20%	1/5	5 : 4	× 4/5
−25%	1/4	4 : 3	× 3/4
−28.56%	2/7	7 : 5	× 5/7
−33.33%	1/3	3 : 2	× 2/3
−50%	1/2	2 : 1	× 1/2

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The Percentage-to-Multiplier Shortcut

Instead of ratios, you can think in terms of a single multiplier:

Change	Multiplier as %	Multiplier as fraction
+20%	120%	6/5
+10%	110%	11/10
+30%	130%	13/10
+25%	125%	5/4
−20%	80%	4/5
−10%	90%	9/10
−30%	70%	7/10
−25%	75%	3/4

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Worked Examples

Example 1: Increase 480 by 25%

• 25% = 1/4, I:F = 4:5
• Method 1: 480 + (480/4) = 480 + 120 = 600
• Method 2: 480 × 5/4 = 600
• Method 3: I:F = 4:5, multiply both by 120 → 480 : 600

Example 2: Decrease a pen's price from 40 by 10%

• 10% = 1/10, I:F = 10:9
• 40 × 9/10 = 36

Example 3: Increase 880 by 12.5%

• 12.5% = 1/8, I:F = 8:9
• 880 × 9/8 = 990

Example 4: Increase 666 by 16.66%

• 16.66% = 1/6, I:F = 6:7
• 666 × 7/6 = 777

Example 5: Student scored 160 marks. Decreased by 12.5%. New marks?

• 12.5% = 1/8, I:F = 8:7
• 160 × 7/8 = 140

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Finding Percentage Change from Two Values

Increase: 48 → 60

• Change = +12
• Method 1: (12/48) × 100 = 25%
• Method 2: 48:60 = 4:5. Difference = 1, base = 4. So 1/4 × 100 = 25%

Decrease: 96 → 84

• Change = −12
• Method 1: (12/96) × 100 = 12.5%
• Method 2: 96:84 = 8:7. Difference = 1, base = 8. So 1/8 × 100 = 12.5%

Decrease: 360 → 300

• 360:300 = 6:5. Difference = 1, base = 6. So 1/6 × 100 = 16.67%

Remember: For percentage change, the base is always the original (initial) value, not the new value.