How to Solve Percentage Word Problems: Discounts, Increases and Original Prices

A student may know that 25% means one quarter but still struggle with a question about discounts or price increases.

The challenge often begins with identifying the starting amount.

Before calculating, ask:

“What quantity represents 100% in this question?”

That question helps distinguish between finding a percentage, changing an amount and working backwards to an original value.

Understand What a Percentage Represents

A percentage expresses a quantity out of 100.

For example:

20% = 20⁄100 = 0.20

To find 20% of AED 150:

0.20 × 150 = AED 30

Here, AED 150 represents the whole amount, or 100%.

AED 30 is the percentage amount. It is not automatically the final price—the question determines what to do next.

Example 1: Find a Discounted Price

A school bag costs AED 240. The shop offers a 15% discount. What is the new price?

First find the discount:

15% of 240 = 0.15 × 240 = AED 36

Subtract the discount from the original price:

AED 240 − AED 36 = AED 204

The bag now costs AED 204.

You can also calculate the remaining percentage directly. After a 15% discount, the customer pays 85%:

0.85 × 240 = AED 204

Both methods give the same result.

Example 2: Calculate a Percentage Increase

A club has 80 members. Membership increases by 25%. How many members does it have now?

Find the increase:

25% of 80 = 20

Add it to the original amount:

80 + 20 = 100 members

Alternatively, the new membership is 125% of the original:

1.25 × 80 = 100 members

Notice the difference between the increase, which is 20 members, and the final total, which is 100.

Example 3: Work Backwards to the Original Price

A jacket costs AED 180 after a 10% discount. What was its original price?

The sale price represents 90% of the original price.

Therefore:

90% = AED 180

Divide by 0.90 to find 100%:

Original price = 180 ÷ 0.90 = AED 200

Check:

10% of AED 200 is AED 20.

AED 200 − AED 20 = AED 180.

A common mistake is adding 10% of AED 180. That uses the discounted price as the starting amount, although the discount was calculated from the original price.

Why Equal Percentage Changes Do Not Cancel Out

Suppose a price increases from AED 100 by 20%:

100 × 1.20 = AED 120

It then decreases by 20%:

120 × 0.80 = AED 96

The final price is AED 96, not AED 100.

The first percentage was calculated from 100. The second was calculated from 120. The percentages are equal, but their starting amounts differ.

Use a Simple Decision Table

Use the table after understanding the situation. A formula is more useful when you can explain why it fits.

Three Checks Before You Finish

First, label your answer. Is it the discount, the increase or the final amount?

Second, check the direction. A discounted price should be lower than the original price.

Third, substitute your result back into the situation, especially when calculating an original value.

Practise With a Small Change

After solving a question, change one detail.

For example, use the same AED 240 bag but change the discount to 25%. Predict whether the final price should be higher or lower before calculating.

Then try a reverse question: if the bag costs AED 180 after a 25% discount, what was the original price?

The answer is AED 240 because:

180 ÷ 0.75 = 240

Get Support With the Reasoning

If percentage questions remain difficult, bring your working to a teacher or tutor. The important step may be identifying the whole amount rather than completing the arithmetic.

You can book a free demo with TheTuitionE to discuss Maths support matched to your child’s grade and curriculum.

Start each problem by finding the 100% amount. That gives the rest of the calculation a clear foundation.