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P6 Working backwards

Today’s problem — free all day, every step. Every day has one.

PSLE 2025 — Zach jacket

  1. (a) Zach bought a jacket at a 15% discount for $57.80. What was the original price before the discount?
  2. (b) Zach's friend later bought the same jacket at a different price. The difference between the two prices was $6.80. What are the two possible discount percentages for his friend's purchase?
One step of the worked solution to PSLE 2025 — Zach jacket, drawn in pencil.
8 steps, drawn in pencil

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The pattern behind it: Working backwards

You know how it ended. Undo each step, last one first.

In this one. Both prices are cut from the same $68, so a $6.80 gap in price is a fixed 10% gap in discount — and because the question never says who paid more, that 10% swings both ways.

What you are toldonly the endleft$12Undo the spendingput the $18 backbefore12 + 18 = 30Undo the givinghalf had gone to Helenat first30 doubled = 60

Also uses: Units and parts

How to spot it

The question gives the final amount after a sequence of changes and asks what the amount was 'at first' or 'to begin with'.

Common mistake

Children undo the steps in the same order they happened rather than in reverse, or forget that a percentage profit is added to the cost price, so the final price is 120% of it, not 100%.

Try one like it

Standard An antique vase — the cost price An antique dealer sold a vase at a 12% profit for $448. What was the cost price of the vase?
All 6 with this pattern →

The 33 problem patterns

All 33 patterns, one to a page — the 19 behind Primary 5 and 6 word problems, and the skills the younger years are built on. The bar model, how to spot it in the question, and the mistake children make. A booklet you can print. Free.

A PDF, and a note when new solutions go up.