Percentage
Sections:
1) Revision notes
2) Practice questions
Revision notes
Percentage basics
How to find the percentage of a number
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} \% $
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 \% $
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 $
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 $
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\% $
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 \% $
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} $
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 $
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: $150$
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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