How To Calculate Percentage Increase In Singapore Maths (Secondary & O Levels Tutorial)

If you’re doing Secondary Maths in Singapore, you already know: percentage questions are everywhere.

Sec 1, Sec 2, E-Maths, A-Maths, N Levels, O Levels – percentage increase shows up in discounts, GST, profit and loss, population growth, and even in some A-Maths application questions.

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The good news? Once you fully understand how to calculate percentage increase (and all its sneaky variants), these questions become very routine marks.

In this tutorial, I’ll walk you through:

• The core method to calculate percentage increase
• How to handle exam-style word problems (not just simple numbers)
• Harder variants that appear in O-Level style questions
• Common mistakes Singapore students make
• How to practise smarter using an AI tutor built for the MOE syllabus

Throughout, I’ll show you how you can use Tutorly.sg – a 24/7 AI tutor website for Singapore students – to drill these skills properly. It’s been mentioned on CNA and used by thousands of students here, so you’re in good company.

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Step-by-step tutorial

Let’s start with the basics and then move into the more “Singapore exam” kind of questions.

1. The core formula for percentage increase

When something increases from an old value to a new value, the percentage increase is:

$\text{Percentage increase} = \frac{\text{Increase}}{\text{Original value}} \times 100\%$

Where:

• $\text{Increase} = \text{New value} - \text{Original value}$
• The original value is always the “before” amount.

Simple example

The price of a file increases from $4 to$5. Find the percentage increase.

1. Original value = $4
2. New value = $5
3. Increase = $5 - 4 = 1$
4. Percentage increase $= \dfrac{1}{4} \times 100\% = 25\%$

So, the price increased by $25\%$.

You’ll see this exact pattern in Sec 1/2 tests and as part (a) of harder O-Level questions.

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2. Converting between “increase by %” and “new value”

You also need to be comfortable with the reverse direction:

• Given the percentage increase, find the new value, or
• Given the new value and the percentage increase, find the original value (this one is trickier and very common in exams).

(a) Given percentage increase, find new value

Formula:

$\text{New value} = \text{Original value} \times (1 + \frac{\text{percentage increase}}{100})$

Example:

A shirt costs $60. The price is increased by $15\%$. Find the new price.

• Increase factor $= 1 + \dfrac{15}{100} = 1.15$
• New price = 60 \times 1.15 = \69$

This “multiply by factor” method is faster than doing it in two steps.

(b) Given new value, find original value (reverse percentage)

This is the one that traps many students.

If something increased by $p\%$ to become a new value, then:

$\text{New value} = \text{Original value} \times (1 + \frac{p}{100})$

So:

$\text{Original value} = \frac{\text{New value}}{1 + \frac{p}{100}}$

Example:

After a $20\%$ increase, a bag costs $72. What was the original price?

• Increase factor $= 1 + \dfrac{20}{100} = 1.2$
• Original price $= \dfrac{72}{1.2} = 60$

So the bag originally cost $60.

This kind of reverse-percentage question appears in Sec 2 and O-Level E-Maths Paper 1 frequently.

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3. Percentage increase vs percentage of

One common confusion: “percentage increase” is not the same as “percentage of”.

• “$x\%$ of $y$” → multiply: $\dfrac{x}{100} \times y$
• “Percentage increase from $a$ to $b$” → use: $\dfrac{b - a}{a} \times 100\%$

Example:

• $20\%$ of $50 = $0.2 \times 50 = 10$
• Percentage increase from $50 to$60 = $\dfrac{60 - 50}{50} \times 100\% = 20\%$

Same numbers, different context, different meaning.

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4. Percentage increase in real-life contexts (Singapore style)

In Singapore exams, percentage increase is often wrapped in real-life contexts:

• GST $8$
• Salary increments
• Population growth
• Price increase after discount
• Profit and loss

Let’s see a typical O-Level style example.

Example (O-Level style):

The price of a laptop is $1500. During a sale, it is sold at a $10\%$ discount. After the sale, the price is increased by $15\%$. Find the overall percentage increase or decrease from the original price.

Step 1: Find sale price after $10\%$ discount.
Discount factor $= 1 - 0.10 = 0.9$

$\text{Sale price} = 1500 \times 0.9 = 1350$

Step 2: After the sale, price increases by $15\%$.
Increase factor $= 1 + 0.15 = 1.15$

$\text{New price} = 1350 \times 1.15 = 1552.50$

Step 3: Compare new price with original.

• Increase $= 1552.50 - 1500 = 52.50$
• Percentage increase $= \dfrac{52.50}{1500} \times 100\% = 3.5\%$

So overall, there is a $3.5\%$ increase from the original price.

Notice you cannot just do $-10\% + 15\% = 5\%$. That’s wrong. In exams, they love to test this.

If you want to practise more of these realistic MOE-style questions, you can use Tutorly.sg’s AI tutor. Just ask for “O Level percentage increase questions with discounts and GST” and it will generate questions and step-by-step worked solutions aligned to the syllabus.

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Exam strategy guide

Understanding the formula is not enough. For N/O-Level exams, you need to be fast, accurate, and careful with wording.

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Here’s how to handle percentage increase questions under exam pressure.

1. Identify “before” and “after” clearly

Always ask yourself:

• What is the original value?
• What is the new value?

Once you are clear, you will know what to put in the denominator.

Example:

A quantity increases from 80 to 92. What is the percentage increase?

• Original value = 80
• New value = 92
• Increase = $92 - 80 = 12$
• Percentage increase $= \dfrac{12}{80} \times 100\% = 15\%$

If you accidentally use 92 as the denominator, you’ll get the wrong answer.

Exam habit: Underline the “before” value in the question. Train yourself to do this during practice.

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2. Translate words into maths step-by-step

Some O-Level questions are wordy. Don’t panic. Break them down.

Example (structured question style):

In 2020, the population of a town was 25 000. In 2023, the population was 28 750.
(a) Find the percentage increase in population from 2020 to 2023.
(b) Hence, or otherwise, find the population in 2026 if the same percentage increase continues every 3 years.

Part (a)

• Original value = 25 000
• New value = 28 750
• Increase = $28 750 - 25 000 = 3 750$
• Percentage increase $= \dfrac{3750}{25 000} \times 100\% = 15\%$

Part (b)

If the same $15\%$ increase continues every 3 years:

• 2020 → 2023: multiply by $1.15$
• 2023 → 2026: multiply by $1.15$ again

So:

$\text{Population in 2026} = 28 750 \times 1.15 = 33 062.5 \approx 33 063$

(Depending on the paper, you may round to the nearest whole number.)

Notice how the percentage increase becomes a multiplier in part (b). This pattern is very common in O-Level Paper 2.

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3. Decide when to use factor vs formula

You basically have two main approaches:

1. Use the factor method: multiply by $(1 + \dfrac{p}{100})$ or $(1 - \dfrac{p}{100})$
2. Use the formula: $\dfrac{\text{increase}}{\text{original}} \times 100\%$

Use factor when:

• You’re given a percentage increase and need the new value
• You have multiple steps (e.g. discount then GST then markup)
• You’re dealing with repeated increases (compound percentage)

Use formula when:

• You’re given both old and new values and asked for the percentage increase
• The question explicitly says “Find the percentage increase…”

In exams, switching between these smoothly saves time.

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4. Show working clearly to secure method marks

In O-Level E-Maths, even if your final answer is wrong, you can still earn method marks if your working is clear.

When dealing with percentage increase:

• Always write at least one clear fraction step, e.g.
  $\dfrac{3750}{25 000} \times 100\%$
• Label your values: “Increase = …”, “Original = …”
• For factor method, show the factor: “Factor $= 1 + 0.15 = 1.15$”

If you practise on Tutorly.sg, you can compare your steps with the AI tutor’s step-by-step solution. It won’t mark every line of your working, but it will show you a proper, exam-standard method so you can adjust your own style.

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5. Manage calculator use wisely

Most percentage increase questions are calculator-allowed, but you should still know:

• How to simplify fractions before pressing the calculator (to reduce careless errors)
• How to round correctly to the number of decimal places / significant figures stated in the question

Example:

You get $\dfrac{3750}{25 000} \times 100\%$.

You can simplify first:

• $\dfrac{3750}{25 000} = \dfrac{375}{2500} = \dfrac{3}{20} = 0.15$
• So percentage $= 0.15 \times 100\% = 15\%$

If you’re rushing in exams, you can key in the full fraction, but always double-check that you didn’t type wrongly.

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Worksheet practice

To really master percentage increase for N/O Levels, you need to practise a mix of:

• Straightforward calculation questions (to build speed)
• Word problems (to build understanding)
• Harder variants (reverse percentage, repeated changes, combined changes)

Here are some practice questions you can try. After each set, I’ll show the answer so you can check.

If you want more, you can go to Tutorly.sg and ask the AI tutor to “generate 10 O-Level percentage increase practice questions with step-by-step solutions”. It will instantly create fresh questions for you.

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A. Basic skills (warm-up)

1. A number increases from 40 to 54. Find the percentage increase.
2. The price of a book is $18. It is increased by $12\%$. Find the new price.
3. After a $25\%$ increase, the cost of a jacket is $75. Find the original cost of the jacket.
4. A school’s enrolment increases from 1200 students to 1380 students. Find the percentage increase in enrolment.

Answers:

1. Increase $= 54 - 40 = 14$
   Percentage increase $= \dfrac{14}{40} \times 100\% = 35\%$

2. Factor $= 1 + 0.12 = 1.12$
   New price = 18 \times 1.12 = \20.16$

3. Factor $= 1 + 0.25 = 1.25$
   Original cost = \dfrac{75}{1.25} = \60$

4. Increase $= 1380 - 1200 = 180$
   Percentage increase $= \dfrac{180}{1200} \times 100\% = 15\%$

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B. Application questions (O-Level style)

5. The price of a washing machine is $820. It is increased by $7\%$. Find the new price, correct to the nearest cent.

6. A shop sells a bag for $96 after a $20\%$ increase in price.
   (a) Find the original price of the bag.
   (b) The shop later offers a $15\%$ discount on the new price of $96. Find the final price of the bag.

7. In 2022, a company’s revenue was $2.4 million. In 2023, the revenue increased by $18\%$.
   (a) Find the revenue in 2023.
   (b) Find the percentage increase in revenue from 2022 to 2024 if the revenue in 2024 is $3.1 million.

Answers (with brief working):

5. Factor $= 1 + 0.07 = 1.07$
   New price $= 820 \times 1.07 = 877.4$
   So new price = \877.40$

(a) Factor $= 1 + 0.20 = 1.20$
Original price $= \dfrac{96}{1.20} = 80$
Original price = \80$

(b) Discount factor $= 1 - 0.15 = 0.85$
Final price = 96 \times 0.85 = \81.60$

(a) Revenue in 2023 $= 2.4 \times (1 + 0.18) = 2.4 \times 1.18 = 2.832$ million

(b) From 2022 to 2024:

• Original value $2022$ = 2.4 million
• New value $2024$ = 3.1 million
• Increase $= 3.1 - 2.4 = 0.7$ million
• Percentage increase $= \dfrac{0.7}{2.4} \times 100\% \approx 29.17\%$
  (Depending on question, you might round to $29.2\%$ or $29\%$.)

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C. Hard exam variants (for O Levels & stronger Sec 3/4)

These are the types that separate A 1 from B 3 in O-Level E-Maths. Try them seriously before checking the solutions.

Question 8: Combined percentage changes

The price of a mobile phone is $1200. During a promotion, the price is decreased by $15\%$. After the promotion, the reduced price is increased by $10\%$.

(a) Find the price of the phone after both changes.
(b) Find the overall percentage change from the original price.

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Question 9: Reverse percentage with profit

A shopkeeper bought some calculators at a certain price each. He increased the selling price by $40\%$ and sold all of them. His total revenue from selling the calculators was $1680.

(a) If each calculator was sold at $42, how many calculators did he sell?
(b) Find the original cost price of each calculator before the $40\%$ increase.

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Question 10: Repeated percentage increase (compound)

The population of a town was 50 000 in 2018. It increases by $4\%$ each year.

(a) Find the population in 2019.
(b) Find the population in 2021.
(c) Find the total percentage increase from 2018 to 2021.

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Question 11: Tricky “percentage of a percentage” style

The price of a TV set is increased by $p\%$ from $800 to$880.

(a) Find the value of $p$.
(b) The new price of $880 is then increased by a further $p\%$. Express the final price in terms of $p$.
(c) If the final price is $968, find the value of $p$.

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Suggested solutions for hard variants

Try them first. Then compare with these worked outlines.

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Q 8 Solution

Original price = $1200

Step 1: Decrease by $15\%$

• Factor $= 1 - 0.15 = 0.85$
• Reduced price $= 1200 \times 0.85 = 1020$

Step 2: Increase by $10\%$

• Factor $= 1 + 0.10 = 1.10$
• Final price $= 1020 \times 1.10 = 1122$

(a) Final price = $1122

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(b) Overall percentage change:

• Original = 1200
• New = 1122
• Change $= 1122 - 1200 = -78$ a decrease of $78
• Percentage change $= \dfrac{-78}{1200} \times 100\% = -6.5\%$

So there is an overall $6.5\%$ decrease.

Common mistake: Students just do $-15\% + 10\% = -5\%$. That’s wrong because the second change is applied to a different base.

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Q 9 Solution

We’re told:

• Selling price is after a $40\%$ increase
• Final selling price per calculator = $42
• Total revenue = $1680

(a) Number of calculators:

$\text{Number} = \frac{1680}{42} = 40$

So he sold 40 calculators.

(b) Original cost price per calculator:

Let original cost price be $C$.

After a $40\%$ increase:

$\text{Selling price} = C \times 1.40 = 42$

So:

$C = \frac{42}{1.40} = 30$

Original cost price = $30 per calculator.

This is a classic reverse-percentage profit question you’ll see in Sec 3/4 tests.

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Q 10 Solution

Population in 2018: 50 000
Yearly increase: $4\%$

(a) 2019

Factor $= 1 + 0.04 = 1.04$

$\text{2019 population} = 50 000 \times 1.04 = 52 000$

(b) 2021

From 2018 to 2021 is 3 years of increase.

You can either:

• Step year by year, or
• Use compound factor $(1.04)^3$

Method 1 $step-by-step$:

• 2018 → 2019: $50 000 \times 1.04 = 52 000$
• 2019 → 2020: $52 000 \times 1.04 = 54 080$
• 2020 → 2021: $54 080 \times 1.04 = 56 243.2$

So population in 2021 $\approx 56 243$ (if rounding to nearest whole number).

Method 2 (direct):

$\text{2021 population} = 50 000 \times (1.04)^3 \approx 50 000 \times 1.124864 = 56 243.2$

(c) Total percentage increase from 2018 to 2021

• Original = 50 000
• New ≈ 56 243.2
• Increase ≈ $56 243.2 - 50 000 = 6 243.2$

Percentage increase:

$\frac{6243.2}{50 000} \times 100\% \approx 12.49\% \approx 12.5\%$

So the total percentage increase over 3 years is about $12.5\%$.

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Q 11 Solution

(a) From $800 to$880:

Increase $= 880 - 800 = 80$

Percentage increase:

$p = \frac{80}{800} \times 100\% = 10\%$

So $p = 10$.

(b) New price after first increase is $880. Increase again by $p\%$.

Factor for second increase $= 1 + \dfrac{p}{100}$

Final price $= 880 \times \left(1 + \dfrac{p}{100}\right)$

That is the expression in terms of $p$.

(c) Final price is $968, and we already know $p = 10$ from part (a). But assume we didn’t know and solve using algebra:

$880 \left(1 + \frac{p}{100}\right) = 968$

Divide both sides by 880:

$1 + \frac{p}{100} = \frac{968}{880} = 1.1$

So:

$\frac{p}{100} = 1.1 - 1 = 0.1 \Rightarrow p = 10$

This question tests your understanding that percentage increase can be represented as $(1 + \dfrac{p}{100})$, and you must be comfortable with algebra and fractions.

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If you want more hard variants like these, you can keep asking Tutorly.sg for “harder O-Level percentage increase questions involving compound changes” and it will keep generating new ones with full worked solutions. This is especially useful when you’ve finished your school worksheet and need more practice targeted at your weak spots.

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Common mistakes

Even strong students lose marks on percentage increase because of small but painful errors. Here are the big ones to watch out for.

1. Using the wrong base (denominator)

Example:

Increase from 80 to 92.

Some students do:

$\frac{92 - 80}{92} \times 100\%$

This is wrong because the denominator must be the original value $80$, not the

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