Cost is the amount used as the purchase or production cost in the simplified question. Selling price is what the item sells for. When selling price exceeds the stated cost, the difference is profit in that model. For cost forty and selling price fifty, profit is ten dollars.

These are three different amounts. A child may calculate the difference correctly but still form the wrong percentage. Keep labels beside the numbers: cost $40, selling price $50, profit $10. Do not describe fifty as the profit or assume that a percentage answer can be found before the question’s comparison base is clear.

Profit as a percentage of cost asks how large the profit is relative to the original cost. Cost is the whole being treated as 100%. Ten dollars is one quarter of forty dollars, so the profit is 25% of cost. The fraction is profit/cost, multiplied by 100%.

A useful check is to rebuild the selling price from that statement: 25% of $40 is $10, and $40 + $10 = $50. If a proposed 20% profit on cost were used instead, the profit would be $8 and selling price $48. That reconstruction exposes the changed reference amount.

No. It is correct when the task explicitly asks for profit as a percentage of selling price. In the same simplified example, 10/50 × 100% = 20%. In a simple sales-and-cost comparison this is a profit margin on sales, not the 25% markup on cost.

The two percentages can both be correct descriptions of the same amounts. They are not contradictory because the denominators differ. Avoid teaching a universal rule to divide every profit question by cost regardless of wording. Teach the requested reference first, then use the appropriate definition.

If an item sells for $75 after a 25% profit on cost, the selling price is 125% of cost. Therefore cost = 75/1.25 = $60. Profit is $15, and 15/60 = 25%. Subtracting 25% of seventy-five would use selling price as the base instead.

If the question instead specifies a profit equal to 20% of selling price, profit is $15 and cost is again $60. These two descriptions happen to match the same sale because 25% on cost and 20% on sales are equivalent here. They are not interchangeable percentages in general.

For an item costing $80 and selling for $68, the loss amount is $12. Loss as a percentage of cost is 12/80 × 100% = 15%. If the question asks for the signed percentage change from cost to selling price, it is −15%. State whether the answer is a loss magnitude or a signed change.

The word loss should not make the denominator negative. The cost remains the positive reference amount in this example. Rebuild the sale as 85% of eighty, giving sixty-eight. This connects a loss percentage to the same original-base reasoning used for a profit.

A school-style example may define profit simply as selling price minus the given cost. Use that model when it is explicitly the task. If delivery, commissions or other costs are supplied and the question asks for profit after those costs, include the stated relevant amounts rather than ignoring them.

Do not invent taxes, fees or accounting classifications that the question does not mention. Conversely, do not present a toy calculation as a complete account of a real business. The learning point is the denominator and the stated model. Clear assumptions make the mathematical answer precise without overclaiming what it describes.

Question 1: cost $30 and selling price $36; find profit as a percentage of cost. Question 2: for the same amounts, find profit as a percentage of selling price. Question 3: an item sells for $96 after a 20% profit on cost; find cost. Question 4: cost $50 and selling price $42.50; find loss percentage on cost.

Answers: 1) 6/30 × 100% = 20%. 2) 6/36 × 100% = 16⅔%. 3) 96/1.2 = $80. 4) 7.50/50 × 100% = 15%. Ask your child to name the 100% amount and reconstruct one selling price as a check.

Bring one question where the profit amount was correct but the denominator was not. A note such as ‘uses selling price although the task asks percentage of cost’ identifies a precise learning need. In a small-group 3-pax lesson, learners can calculate both comparisons and explain why the answers differ.

For parents considering Secondary 1 Mathematics tuition in Punggol, the next-question routine is to label the amounts, identify the reference whole, form the fraction and check by rebuilding the price. A correct comparison is more useful than a memorised percentage rule detached from its denominator.