Today’s problem — free all day, every step. Every day has one.
Bicycle shop — sold at a profit
A bicycle shop sold a bicycle at a 25% profit for $250. What was the cost price of the bicycle?
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The cost price was $200.
The pattern behind it: Working backwards
You know how it ended. Undo each step, last one first.
In this one. The percentage is always measured from the cost price, so the cost price is 100% and the selling price is 125% — match the $250 to its own percentage before dividing.
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?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.