When a percentage is taken from what remains, the whole changes between steps. To work backwards, label the final amount with the percentage left at the second step. Find the amount before that step, then use the first percentage to recover the original total.
This PSLE Mathematics guide applies primary percentage and part-whole reasoning to a two-step problem. It uses a whole-number model so pupils can see what counts as 100% each time.
- Underline ‘of the remainder’ and label the new whole.
- Find the percentage left after the second action.
- Use the final amount to recover the first remainder.
- Use that remainder to recover the starting amount and check forwards.
CHAPTER 1 OF 4 · Back to contents
Name the whole every time
Suppose a stall sells 40% of its original muffins in the morning. The morning remainder is 60% of the starting stock. When the stall sells 25% of that remainder, the 25% describes the morning remainder. In the afternoon calculation, the morning remainder is the whole.
Keep two lines in your working. Write ‘morning: original stock’ on one line and ‘afternoon: stock after morning’ on the next. Each line has its own 100%. This makes it easier to see which amount each percentage refers to.
After selling 25% in the afternoon, the stall keeps 75% of what it had at midday. Work backwards from that relationship first because the question tells you what was left at the end.
CHAPTER 2 OF 4 · Back to contents
Worked example | Recover the original stock
A stall sells 40% of its muffins in the morning and 25% of the remainder in the afternoon. It has 54 muffins left after both sales. How many muffins did the stall start with?
| Step | What counts as 100%? | Percentage left from that whole |
|---|---|---|
| Morning sale | Original stock | 60% |
| Afternoon sale | Stock after the morning sale | 75% |
In the afternoon, 75% is three quarters. Three equal parts are 54 muffins, so one part is 18. All four parts make 72 muffins. That was the stock after the morning sale.
The 72 muffins are 60% of the original stock. Since 60% is three fifths, three equal parts are 72 and one part is 24. Five parts give 120 muffins at the start.
Check forwards. The morning sale is 40% of 120, or 48, leaving 72. The afternoon sale is 25% of 72, or 18, leaving 54.
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CHAPTER 3 OF 4 · Back to contents
Practise with a fresh remainder
A box starts with an unknown number of cards. Mina gives away 20% of the original cards, then gives away 25% of the cards still in the box. She has 48 cards left. Find the original number.
After the second action, 48 is three quarters of the first remainder. One quarter is 16, so the first remainder is 64. That is four fifths of the original number, so one fifth is 16 and the original number is 80.
For a check, follow the cards forwards. Mina gives away 16 of the 80 cards first, leaving 64. She gives away one quarter of 64, which is 16, and keeps 48. In this example the two actions remove the same number of cards even though the percentages differ.
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CHAPTER 4 OF 4 · Back to contents
Frequently asked questions
Why does adding 40% and 25% give a different answer?
Those percentages refer to different wholes. In the muffin example the afternoon sale is 18 out of the original 120, or 15% of the original. On the same base, the combined sale is 40% + 15% = 55%.
What if both percentages are explicitly of the original amount?
Then they share one base. If the amounts removed are separate, add their percentages to find the total removed from that original whole.
What can a parent ask before checking the arithmetic?
Ask what counts as 100% in each sentence. Then ask the pupil to name what the given final amount represents.
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Sources and next reading
SEAB PSLE Mathematics examination syllabus, applicable from 2026