Arithmetic Problems

Percentage, discount, commission and tax: the four money calculations

By Mr Gan · O-Level E Maths · Updated August 2026 · 7 min read

Why students lose marks here

Most students can find 15% of a number. Where the marks go is the second step: knowing whether that 15% should be subtracted, added, or is the answer on its own. A discount question and a GST question use identical arithmetic up to the last line and then go in opposite directions.

The other habit that costs marks is doing it in two steps: find the discount, then subtract it. That works, but it doubles the chances of a rounding slip and it is slower. The multiplier method does it in one step and is far harder to get wrong.

The method

The word to hunt for is the one that tells you what the percentage is of. Commission is a percentage of sales, not of salary. A discount is a percentage of the marked price, not of the price you end up paying. Getting that base right is most of the battle.

Worked example 1: discount

A jacket is marked at $180. A shop offers 25% off. Find the sale price.

Worked example 2: commission

A salesperson earns a basic wage of $1200 per month plus 4% commission on all sales. In one month she sells $65 000 worth of goods. Find her total income.

Worked example 3: GST added on

A meal costs $48 before tax. GST of 9% is added. Find the total bill.

Worked example 4: percentage change

A phone that cost $750 last year now costs $690. Find the percentage decrease.

Notice the base again: dividing by 690 instead of 750 gives 8.7%, which is wrong. Percentage change is always out of what you started with. If instead you are given the final price and the rate, and asked for the original, that is the reverse case, covered in reverse percentage problems.

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Frequently asked questions

What is the multiplier method?

Instead of finding the percentage and then adding or subtracting it, you multiply by a single number. A 25% discount means multiplying by 0.75. A 9% tax means multiplying by 1.09. One step, one rounding, fewer mistakes.

How do I do successive discounts?

Multiply the multipliers. A 20% discount followed by a further 10% off is × 0.8 × 0.9 = × 0.72, which is a 28% discount overall, not 30%. This is the question examiners use to catch students who add the percentages.

Is commission taken before or after tax?

For O-Level purposes, treat each instruction in the order the question gives it. Read the sentence order carefully: "4% commission on sales" always means 4% of the sales figure quoted, and anything else in the question is added afterwards.

Why can I not just add percentages?

Because the second percentage is taken of a different amount. After a 20% discount you are working from 80% of the original, so a further 10% is 10% of that smaller number. Percentages only add when they are percentages of the same base.

How does this connect to the rest of E-Maths?

The multiplier is the same idea that powers simple and compound interest, where you multiply by (1 + r/100) once per year. It also underpins rates, profit and loss, where profit is a percentage of cost price.

— Mr Gan Math Tuition