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Percentage basics

How to find the percentage of a number

Example

Calculate $67\%$ of $\$ 123$.

Answer: $ \$ 82.41 $

Solutions

How to express one quantity as a percentage of another

Example

Out of $120$ silicon chips produced, $5$ were found to be defective. Calculate the percentage of the chips that are not defective.

Answer: $ 95{5 \over 6} \% $

Solutions

Percentage change

Find percentage change

$ \text{Percentage change = }$ $ {\text{Final} - \text{Initial} \over \text{Initial} } \times 100 $

Example

An iPhone originally cost $ \$ 2000 $. If the price was reduced to $ \$ 1700 $, find the percentage decrease in price.

Answer: $ 15 \% $

Solutions

Find new quantity given percentage change

Example

$22400$ students took the O Level examinations in $2024$. In $2025$, $1\%$ more students took the O Level examinations. How many students took the O Level examinations in $2025$?

Answer: $ 22624 $

Solutions

Percentage in real-world context

Profit

If an item is sold at $ 110 \% $ profit on the cost price, the selling price is $ 210 $ $ \%$ of the cost price.


Loss

If an item is sold $ 45 \% $ loss on the cost price, the selling price is $ 55 $ $ \%$ of the cost price.


Discount

If an item is sold at $11 \%$ discount, the discounted price is $ 89 $ $ \%$ of the marked price.


Goods and Services Tax (GST)

If there's $9 \%$ GST charged on an item, the price after GST is $ 109 $ $ \%$ of the selling price.

Reverse percentage

Example

In $2026$, there were $1452$ students enrolled in a language school.

The enrolment in $2026$ was $10\%$ more than in $2025$. Find the number of students enrolled in $2025$.

Answer: $ 1320 $

Solutions


Practice questions

Percentage change without actual values

1. If the length of a cube is increased by $10 \% $, find the percentage increase in its volume.

Answer: $ 33.1\% $

Solutions


2. If the length of a rectangle is increased by $ 15 \%$ and the breadth of the same rectangle is decreased by $ 20 \%$, find the percentage change in its area.

Answer: $ -8 \% $

Solutions

Word problems in real-world context involving percentage

Reverse percentage

3. Brian's 2.4 km run timing in $2026$ was $9$ minutes $54$ seconds.

His timing in $2026$ was $10\%$ less than his timing in $2025$.

His timing in $2025$ was $34\%$ less than his timing in $2024$.

What was Brian's 2.4 km run timing in $2024$? Leave your answer in minutes and seconds.

Answer: $ \text{16 minutes 40 seconds} $

Solutions

Combining reverse percentage with profit and discount

4. Jim bought a mountain bike for $\$180$ to sell at his shop.

The marked price of the bike is set such that he can offer a $10\%$ discount and still make a $20\%$ profit.

Find the marked price of the bike.

Answer: $ \$240 $

Solutions

Percentage of the remaining quantity

5. A bakery made some pastries in the morning.

$ 40 \% $ of the pastries were croissants.

$60\%$ of the remaining pastries were curry puffs.

The other $36$ pastries were egg tarts.

How many pastries did the bakery make in the morning?

Answer: $150$

Solutions


O Level past year questions on percentage

Year & paper Comments
2024 P2 Question 2b Word problem in real-world context - Percentage change
2023 P1 Question 7 Word problem in real-world context - Percentage of the remaining quantity
2021 P1 Question 8 Word problem in real-world context - Percentage change
2021 P2 Question 2c, d Word problem in real-world context - Percentage change
2020 P1 Question 14 Word problem in real-world context - Percentage of the remaining quantity
2019 P2 Question 3b Word problem in real-world context - Reverse percentage
2018 P2 Question 2a Word problem in real-world context - Percentage change
2017 P2 Question 2 Word problem in real-world context - Percentage change, Reverse percentage
2015 P1 Question 2 Word problem in real-world context - Profit
2015 P1 Question 10 Word problem in real-world context - Percentage change
2015 P2 Question 3a, bi Word problem in real-world context - Commission, Loss
2014 P1 Question 9 Word problem in real-world context - Percentage change
2014 P2 Question 2 Word problem in real-world context - Percentage change, Reverse percentage
2013 P1 Question 11 Word problem in real-world context - Percentage of the remaining quantity
2012 P2 Question 4b Word problem in real-world context - Percentage change
2011 P1 Question 6b Express one quantity as a percentage of another
2010 P1 Question 1 (a) Express fraction as percentage
(b) Express percentage as fraction
2010 P2 Question 3c Word problem in real-world context - Percentage of the remaining quantity
2009 P1 Question 2 Word problem in real-world context - Profit
2009 P1 Question 4a Express one quantity as a percentage of another
2009 P2 Question 1b Word problem in real-world context - Reverse percentage
2007 P1 Question 3a Express fraction as percentage
2007 P1 Question 7 Percentage change without actual values
2007 P2 Question 1c Word problem in real-world context - Percentage change
2006 P1 Question 4 Express one quantity as a percentage of another
2006 P1 Question 5b Word problem in real-world context
2006 P2 Question 5b, c Word problem in real-world context
2005 P1 Question 4b Express one quantity as a percentage of another
2005 P1 Question 13a Word problem in real-world context - Percentage change


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