Discount and Markup — Revision Notes

⚡ 30-Second Revision

Markup uses cost; discount uses marked price.
Profit percentage normally uses cost.
Multiply successive price factors.
Undo a change by dividing by its factor.
Margin on sales is a different denominator.

2-Minute Revision

Track cost, marked price and selling price separately. A 40% markup followed by a 20% discount gives 1.4 × 0.8 = 1.12 times cost, hence 12% profit on cost. The same profit divided by selling price is a different percentage. Successive discounts combine multiplicatively, and reversing a discount requires division rather than adding the same percentage to the reduced amount. Do not include taxes or expenses unless the exercise supplies them.

5-Minute Revision

An item costs 1,200. A seller wants 20% profit after offering a 10% discount. The target selling price is 1,440 and the marked price must be 1,440/0.9 = 1,600. The markup is 400/1,200 = 33⅓%. Check by applying the discount to 1,600. Explain why a 30% markup is insufficient: it produces 1,560 before discount and 1,404 after discount, which is 17% profit on cost.

Vyyuha Quick Recall

C → M → S: label the price chain, then attach each percentage to its own base.