Discount and Markup — Fundamental Concepts

Fundamental Concepts

Name the three prices

Cost price is the seller's stated acquisition cost in the exercise. Marked price is the price before the specified discount. Selling price is what the customer pays after that discount. Additional charges should enter only when the question supplies them and explains their treatment.

Use multipliers

If cost is 800 and the markup is 25%, marked price is 800 × 1.25 = 1,000. A 10% discount gives a selling price of 900. Profit is 100, which is 12.5% of cost. The markup and discount cannot be subtracted as though both used the same base.

Two discounts of 20% and 10% leave 0.8 × 0.9 = 0.72 of the original marked price. The equivalent discount is 28%, not 30%. Reversing their order gives the same final multiplier when no intermediate rounding or other condition changes the calculation.

Work backwards carefully

If a selling price of 900 follows a 10% discount, the marked price is 900/0.9 = 1,000. Adding 10% to 900 produces 990 and uses the wrong base. For a required profit, first compute the target selling price from cost and then divide by the discount factor to obtain the necessary marked price.

Check whether a question asks for profit on cost or margin on sales. The same monetary profit produces different percentages under those denominators.