Marked price, discount and markup

Learning outcome

Connect cost, marked price and actual selling price while distinguishing markup, profit percentage and profit margin.

Three prices and their percentage bases

Cost price (CP) includes stated overheads. Marked price (MP) is the listed price before discount. Selling price (SP) is the amount received after discount. Use positive prices here and ignore taxes or unstated charges.

Discount amount = MP - SP.

Discount percentage = (discount amount ÷ MP) × 100.

A d% discount leaves SP = MP × (1 - d/100), because the buyer pays the portion remaining after the reduction. The discount base is MP, not CP.

Markup is the increase used to set MP above cost:

Markup percentage = [(MP - CP) ÷ CP] × 100.

Profit percentage measures actual profit on cost, whereas profit margin measures it on actual sales receipts:

Profit percentage = [(SP - CP) ÷ CP] × 100.

Profit margin percentage = [(SP - CP) ÷ SP] × 100.

Markup is not guaranteed profit: a later discount reduces what the seller receives. Margin and profit percentage also differ because their denominators differ. For positive profit, margin is smaller than profit percentage since SP exceeds CP.

These rates answer different questions: how far the label sits above cost, how much the investment gains, and how much of each unit of sales revenue remains as profit.

To set a marked price for a target profit, first find the required SP from cost. Then divide that SP by the fraction retained after discount. Use discounts below 100% so the divisor remains positive.

Worked examples

Example 1 — Calculate a discount. An item marked ₹1,750 has a 12% discount. Discount = 1750 × 0.12 = ₹210. SP = 1750 - 210 = ₹1,540. The percentage is taken from the listed price.

Example 2 — Separate three rates. CP is ₹900 and markup is 50%. MP = 900 × 1.50 = ₹1,350. A 20% discount gives SP = 1350 × 0.80 = ₹1,080. Profit = ₹180; profit percentage = (180 ÷ 900) × 100 = 20%. Margin = (180 ÷ 1080) × 100 = 16 2/3%, exactly. The markup, profit percentage and margin are different measures.

Example 3 — Set the marked price. Effective CP is ₹1,575. A seller wants 20% profit after giving 25% discount. Required SP = 1575 × 1.20 = ₹1,890. Since the buyer pays 75% of MP, MP = 1890 ÷ 0.75 = ₹2,520. Check: 2520 × 0.75 = ₹1,890.

Common mistakes

Do not subtract discount percentage directly from markup percentage; their bases differ. Do not calculate margin using MP. A discount describes a reduction from the listed price, not necessarily a loss on cost.

Practice questions

1. An item marked ₹2,350 receives a 12% discount. Find the discount amount and SP.
2. CP is ₹1,250. Find MP after a 28% markup.
3. CP is ₹1,440 and SP is ₹1,800. Find profit percentage and profit margin.
4. Effective CP is ₹1,600. What MP allows 17% profit after a 22% discount?

Worked answers

1. Discount = 2350 × 0.12 = ₹282. SP = 2350 - 282 = ₹2,068.
2. Markup = 1250 × 0.28 = ₹350. MP = 1250 + 350 = ₹1,600.
3. Profit = 1800 - 1440 = ₹360. Profit percentage = (360 ÷ 1440) × 100 = 25%; margin = (360 ÷ 1800) × 100 = 20%.
4. Required SP = 1600 × 1.17 = ₹1,872. A 22% discount retains 78% of MP, so MP = 1872 ÷ 0.78 = ₹2,400.