PSLE Maths percentage: reverse and chained percentage
Finding 15% of something is a P5 skill. The P6 marks are in the questions that run the other way: given the price after the discount, find the price before. And then do it twice.
What the papers ask
- Percentage of a quantity, and one quantity as a percentage of another. Discount and GST.
- Percentage increase and decrease, always as a percentage of the original amount.
- Reverse percentage: 85% of the price is $136, so what was the price?
- Chained reverse percentage: a price marked up and then discounted, worked back to the cost. Two reversals in one question.
- A moving base: 40% of a group are girls, some girls leave, and now 20% are girls. The second percentage is of a smaller group.
The mistakes that cost marks
| Mistake | What to do instead |
|---|---|
| The percentage taken of the amount after, not before | Ask which amount is 100%. For a discount it is the original price, never the price paid. |
| Two percentages added or subtracted | 20% up and 10% down is not 10% up. Apply each to its own whole, one step at a time. |
| The same total used before and after | When some of the group leave, the whole changes. Find what did not change first. |
| The discount given when the price was asked | Underline the question's last sentence before writing the answer. |
| Money rounded too early | Keep the cents until the last line. |
A worked example
A shop marked the price of a bicycle 20% above its cost price. In a sale, it sold the bicycle at 10% off the marked price, for $864.
(a) What was the marked price?
(b) What was the cost price?
(c) The shop's profit was what percentage of the cost price?
What makes it hard: two percentages, each of a different whole, and the question starts at the end.
(a) 10% off means the sale price is 90% of the marked price. 90% = $864, so 1% = $9.60 and 100% = $960.
(b) 20% above cost means the marked price is 120% of the cost price. 120% = $960, so 1% = $8 and 100% = $800.
(c) Profit: $864 − $800 = $64. As a percentage of the cost: 64 ÷ 800 × 100% = 8%. Not 10%, which is the answer from subtracting the percentages.
How to practise percentage
- Before any working, write which amount is 100%.
- Practise reverse questions until "divide by 90, times 100" is automatic, then chain two.
- Do one moving-base question in every session. It is the one most children have not seen.
Percentage is in every paper in our courses, forwards and backwards, marked before each lesson. See the course dates, or read what P6 tuition costs.
Common questions about PSLE percentage
What is reverse percentage in PSLE Maths?
A question that gives the amount after a percentage change and asks for the amount before. After a 10% discount the price is 90% of the original, so the original is the price paid divided by 90 and multiplied by 100. Taking 10% of the price paid and adding it back is the common wrong answer.
Why is 20% more and then 10% off not 10% more?
Because the two percentages are of different amounts. The 20% is of the cost price and the 10% is of the marked price, which is larger. Each percentage has to be applied to its own whole, one step at a time.
Practise it, free
Each is a full Paper 1 and Paper 2, marked the moment it is handed in, with a report on what went wrong.
20 seats. One paper a day.
Online P6 Maths crash courses in the school holidays: one full paper a day, marked before class, a report to parents every night.
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