Percentage Problems in IGCSE Maths – Increase, Decrease, and Reverse

Percentages: Guaranteed Marks

Percentage questions appear on every single IGCSE Mathematics 0580 paper, at both Core and Extended level. They range from straightforward calculations worth one or two marks to more complex reverse percentage problems worth three or four marks. Mastering all types of percentage questions is one of the most efficient ways to improve your exam grade.

This guide covers every percentage question type you will encounter, with worked examples for each.

Type 1: Finding a Percentage of an Amount

This is the most basic percentage calculation and the foundation for everything else.

Method: Convert the percentage to a decimal and multiply.

Worked Example

Find 35% of 240.

35% = 0.35

0.35 × 240 = 84

Answer: 84

Exam tip: You can also use the fraction method: 35/100 × 240 = 84. Use whichever you find quicker and more reliable.

Type 2: Expressing One Quantity as a Percentage of Another

Method: Divide the part by the whole and multiply by 100.

Worked Example

A student scores 42 out of 60 on a test. What is this as a percentage?

(42 ÷ 60) × 100 = 70%

Answer: 70%

Type 3: Percentage Increase

Method: Find the percentage of the original amount and add it on. Or use the multiplier method: multiply by (1 + percentage/100).

Worked Example

A shirt costs RM 80. The price increases by 15%. Find the new price.

Method 1 (two steps):

15% of 80 = 0.15 × 80 = 12

New price = 80 + 12 = RM 92

Method 2 (multiplier):

New price = 80 × 1.15 = RM 92

Both methods give the same answer. The multiplier method is faster and less prone to error, especially in multi-step problems.

The multiplier for a percentage increase is always 1 + (percentage ÷ 100).

• Increase of 20% → multiply by 1.20
• Increase of 5% → multiply by 1.05
• Increase of 120% → multiply by 2.20

Type 4: Percentage Decrease

Method: Find the percentage of the original amount and subtract it. Or use the multiplier method: multiply by (1 - percentage/100).

Worked Example

A laptop costs RM 3,200. It is reduced by 12% in a sale. Find the sale price.

Sale price = 3200 × 0.88 = RM 2,816

The multiplier for a percentage decrease is always 1 - (percentage ÷ 100).

• Decrease of 12% → multiply by 0.88
• Decrease of 25% → multiply by 0.75
• Decrease of 3% → multiply by 0.97

Type 5: Finding the Percentage Change

Method: Percentage change = (change ÷ original) × 100

Worked Example

A house was bought for RM 450,000 and sold for RM 522,000. Calculate the percentage profit.

Change = 522,000 - 450,000 = 72,000

Percentage change = (72,000 ÷ 450,000) × 100 = 16%

Answer: 16% profit

Exam tip: Always divide by the ORIGINAL value, not the new value. This is one of the most common mistakes in percentage questions.

Type 6: Reverse Percentage (Finding the Original)

Reverse percentage questions are where many students lose marks. You are given the value AFTER a percentage change and asked to find the original value.

The key insight: The value you are given represents a specific percentage of the original. You must work backward to find 100%.

Worked Example 1: Reverse Increase

After a 20% price increase, a jacket costs RM 144. Find the original price.

The new price represents 120% of the original (100% + 20%).

120% = RM 144

1% = 144 ÷ 120 = 1.20

100% = 1.20 × 100 = RM 120

Using the multiplier: Original = 144 ÷ 1.20 = RM 120

Answer: The original price was RM 120.

Worked Example 2: Reverse Decrease

In a sale, a television is reduced by 15%. The sale price is RM 1,275. Find the original price.

The sale price represents 85% of the original (100% - 15%).

85% = RM 1,275

1% = 1,275 ÷ 85 = 15

100% = 15 × 100 = RM 1,500

Using the multiplier: Original = 1,275 ÷ 0.85 = RM 1,500

Answer: The original price was RM 1,500.

The classic mistake: Many students calculate 15% of 1,275 and add it back on. This gives 1,275 + 191.25 = 1,466.25, which is WRONG. You cannot add 15% of the sale price because 15% of the sale price is not the same as 15% of the original price.

Worked Example 3: Reverse with VAT/Tax

A bill including 6% SST (Sales and Service Tax) comes to RM 84.80. Find the price before tax.

The bill represents 106% of the pre-tax price.

Original = 84.80 ÷ 1.06 = RM 80.00

Answer: The price before tax was RM 80.00.

Type 7: Repeated Percentage Change (Compound)

When a percentage change happens repeatedly (such as compound interest or depreciation), you apply the multiplier multiple times.

Worked Example: Compound Interest

RM 5,000 is invested at 4% compound interest per year. Find the value after 3 years.

Multiplier for 4% increase = 1.04

Value after 3 years = 5,000 × 1.04³

= 5,000 × 1.124864

= RM 5,624.32

Exam tip: Use the power key on your calculator. Type 5000 × 1.04^3 to get the answer directly. Do not calculate year by year unless the question asks you to show each year’s value.

Worked Example: Depreciation

A car worth RM 60,000 depreciates by 18% each year. Find its value after 4 years.

Multiplier for 18% decrease = 0.82

Value after 4 years = 60,000 × 0.82⁴

= 60,000 × 0.45212176

= RM 27,127.31 (to the nearest cent)

Type 8: Finding the Number of Years

Question: RM 2,000 is invested at 5% compound interest. After how many years will it exceed RM 3,000?

Set up: 2,000 × 1.05ⁿ > 3,000

1.05ⁿ > 1.5

You can solve this by trial and improvement:

• n = 5: 1.05⁵ = 1.2763 (not enough)
• n = 8: 1.05⁸ = 1.4775 (not enough)
• n = 9: 1.05⁹ = 1.5513 (exceeds 1.5)

Answer: After 9 years

Exam tip: On the Extended paper, you might also solve this using logarithms: n = log(1.5) ÷ log(1.05) = 8.31, which rounds up to 9 complete years.

Quick Reference: Percentage Multipliers

Operation	Multiplier	Example
Increase by 25%	× 1.25	200 × 1.25 = 250
Decrease by 25%	× 0.75	200 × 0.75 = 150
Find original after 25% increase	÷ 1.25	250 ÷ 1.25 = 200
Find original after 25% decrease	÷ 0.75	150 ÷ 0.75 = 200

Learn to use multipliers fluently and percentage questions become fast and reliable.

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