Marked Price, Discount and Profit Problems

Discount questions involve three prices. The cost price (CP) is what the shopkeeper paid. The marked price (MP), also called the list or tag price, is what is printed on the item. The selling price (SP) is what the customer finally pays after the discount.

Discount = MP − SP, and the discount percentage is on MP.
Profit = SP − CP, and the profit percentage is on CP.

Almost every mistake in this chapter comes from mixing up those two bases. Hold on to them and the questions become routine.

Worked example 1: SP from MP

A shirt is marked ₹1,200 and sold at a 15% discount. SP = 1,200 × 0.85 = ₹1,020.

Worked example 2: MP from SP

After a 15% discount a pair of shoes costs ₹1,360. MP = 1,360 ÷ 0.85 = ₹1,600. Do not add 15% to the SP: the discount was a percentage of the larger MP.

SP can be written two ways: from the marked price after the discount, and from the cost price after the profit. Setting them equal gives a single equation that links all four quantities.

MP × (100 − discount%) = CP × (100 + profit%)

Rearranged, MP ÷ CP = (100 + profit%) ÷ (100 − discount%). If the question gives any three of MP, CP, discount and profit, this equation gives the fourth in one line. For a loss, replace (100 + profit%) with (100 − loss%).

Worked example 3: finding the marked price

A cooler costs ₹1,500. The dealer wants a 20% profit after a 10% discount. MP = 1,500 × 120 ÷ 90 = ₹2,000.

Worked example 4: how much to mark up

By what percentage above cost should goods be marked to make a 20% profit after a 20% discount? MP ÷ CP = 120 ÷ 80 = 1.5, so the mark-up is 50%.

Worked example 5: a gain despite the discount

A shopkeeper gives a 10% discount and still gains 17%. MP ÷ CP = 117 ÷ 90 = 1.3, so the goods were marked 30% above cost.

When the question gives the mark-up and the discount and asks for the profit, multiply the two multipliers. A mark-up of m% is the multiplier (1 + m/100) and a discount of d% is (1 − d/100).

Worked example 6: 25% up, 10% off

An item costing ₹800 is marked 25% higher and sold at 10% off. 1.25 × 0.90 = 1.125, so the profit is 12.5% (₹100 on ₹800).

Worked example 7: 40% up, 25% off

1.40 × 0.75 = 1.05, a profit of 5%. Simply subtracting 25 from 40 would suggest 15%, three times the true figure.

The same multipliers answer the reverse question: given the mark-up and the profit the seller must keep, what is the largest discount he can offer? Divide the required profit multiplier by the mark-up multiplier, and the shortfall from 1 is the discount.

Worked example 8: the largest discount

Goods are marked 50% above cost, and the seller needs at least a 20% profit. 1.20 ÷ 1.50 = 0.80, so SP may fall to 80% of MP and the largest discount is 20%. Any bigger discount cuts the profit below 20%.

If the discount is larger than the mark-up can absorb, the multiplier product falls below 1 and the seller makes a loss. A 20% mark-up with a 20% discount gives 1.20 × 0.80 = 0.96, a 4% loss, even though the two percentages look equal.

An offer of "buy x, get y free" means the customer receives x + y items and pays for x of them. The free items are the discount, measured against the full value of everything taken.

Effective discount % = y ÷ (x + y) × 100

Worked example 9: buy 4, get 1 free

The customer takes 5 items and pays for 4. The discount is 1 ÷ 5 × 100 = 20%, not 25%.

✘ Taking the discount percentage on CP. Discount is always on MP.
✘ Subtracting the discount from the mark-up to get the profit. Multiply the multipliers.
✘ Using y ÷ x instead of y ÷ (x + y) for "buy x, get y free".
✘ Finding MP from SP by adding the discount percentage to SP.

Start with the profit and loss formulas if CP and SP are still unfamiliar. Two or more discounts in a row are handled by the successive discount formula, and the core results are in the Quant cheat code.

Q1. A jacket marked at ₹2,500 is sold at a 12% discount. What is its selling price? easy

(a) ₹2,200 (b) ₹2,300 (c) ₹2,188 (d) ₹2,120

✅ Answer: (a) ₹2,200

💡 Explanation: The discount is taken on the marked price, so SP = 2,500 × 0.88 = ₹2,200.

Q2. An item costing ₹600 is marked 30% above cost and sold at a 10% discount. What is the profit percentage? easy

(a) 20% (b) 27% (c) 15% (d) 17%

✅ Answer: (d) 17%

💡 Explanation: Multiply the multipliers: 1.30 × 0.90 = 1.17, so SP is 117% of CP and the profit is 17%. Subtracting 10 from 30 to get 20% is wrong.

Q3. A shop offers 'buy 3, get 1 free'. What is the effective discount percentage? medium

(a) 33.33% (b) 25% (c) 30% (d) 20%

✅ Answer: (b) 25%

💡 Explanation: The customer takes 4 items and pays for 3, so 1 of the 4 items is free. The discount is 1 ÷ 4 × 100 = 25%.

Q4. How much above the cost price must a trader mark goods to gain 26% after allowing a 10% discount? medium

(a) 36% (b) 30% (c) 40% (d) 26%

✅ Answer: (c) 40%

💡 Explanation: MP ÷ CP = (100 + 26) ÷ (100 − 10) = 126 ÷ 90 = 1.4, so the goods must be marked 40% above cost.

Q5. After a 15% discount a watch sells for ₹2,040. What was its marked price? easy

(a) ₹2,346 (b) ₹2,400 (c) ₹2,350 (d) ₹2,250

✅ Answer: (b) ₹2,400

💡 Explanation: SP = 0.85 × MP, so MP = 2,040 ÷ 0.85 = ₹2,400. Adding 15% to ₹2,040 gives the wrong ₹2,346.

Q6. A trader buys a table for ₹1,800. He wants a 25% profit after giving a 10% discount. What should the marked price be? hard

(a) ₹2,250 (b) ₹2,475 (c) ₹2,400 (d) ₹2,500

✅ Answer: (d) ₹2,500

💡 Explanation: MP × 90 = CP × 125, so MP = 1,800 × 125 ÷ 90 = ₹2,500. Check: 10% off ₹2,500 is ₹2,250, which is 25% above ₹1,800.

Is discount calculated on cost price or on marked price?

Discount is always calculated on the marked price, the price printed on the tag. Profit and loss are calculated on the cost price. Keeping these two bases separate avoids most mistakes in this chapter.

Why can't I subtract the discount from the mark-up to get the profit?

The two percentages are taken on different bases. The mark-up is on cost price and the discount is on the larger marked price, so the discount removes more rupees than the same percentage of cost. Multiply the multipliers instead.

All problems and solutions on this page are original. No outside facts are relied on; every numeric answer is recomputed by software before publishing.

How this page was prepared. Drafted with AI assistance (Claude (Anthropic AI model)) from the sources listed above. 16 calculations on this page were recomputed by software and matched. Automated checks also covered structure, internal links and duplicate text. Software checks cannot confirm facts. Reviewed by praveenkumar on 2026-10-20 against the sources listed above.

Found an error? Report it and we will correct the page.