Profit, loss and discount questions combine three prices: cost, marked and selling. Enter the cost price, marked price and discount to get the selling price, profit or loss, profit percentage and markup.
Enter the cost price and marked price.
Enter the discount percentage.
Read the selling price and profit or loss.
Selling price: SP = MP × (1 − d ÷ 100)
Profit %: (SP − CP) ÷ CP × 100
Profit and loss links three prices. Cost price (CP) is what the seller paid. Marked price (MP) is the price on the tag. Selling price (SP) is what the buyer actually pays after any discount. This calculator takes CP, MP and the discount percentage and returns SP, profit or loss in rupees, profit or loss percentage on cost, and the markup.
Shopkeepers, small business owners and students preparing for aptitude tests all work with these relationships. A retailer deciding how much discount to offer during a Diwali sale needs to know whether that discount still leaves a profit on cost.
The key convention is that profit and loss percentages are measured on cost price, while discount is measured on marked price.
1. Note the cost price CP, marked price MP and discount d%.
2. Selling price SP = MP × (1 − d ÷ 100).
3. Profit or loss = SP − CP. Positive means profit, negative means loss.
4. Profit or loss % = (SP − CP) ÷ CP × 100.
5. Markup % = (MP − CP) ÷ CP × 100.
6. To find the discount for a target profit p%, set SP = CP × (1 + p ÷ 100) and discount = (MP − SP) ÷ MP × 100.
Discount is a percentage of the marked price, while profit is a percentage of the cost price. Because the bases differ, a markup of 50% followed by a discount of 50% does not bring you back to cost. Starting from CP 100, MP is 150, and after a 50% discount SP is 75, a 25% loss. In general, with markup m and discount d as decimals, SP ÷ CP = (1 + m)(1 − d), so profit % = ((1 + m)(1 − d) − 1) × 100.
The largest discount that still avoids a loss makes SP equal to CP. From MP × (1 − d) = CP, d = 1 − CP ÷ MP = markup ÷ (1 + markup). With a 60% markup, the break-even discount is 0.6 ÷ 1.6 = 37.5%. Any bigger discount means a loss. Retailers use this to set sale limits, and exam questions often ask for it.
Real profit calculations include overheads such as rent, salaries, transport and damage, as well as GST. In business accounting, gross margin is often quoted on selling price rather than cost, which gives a smaller percentage for the same rupee profit. Aptitude questions follow the cost-price convention unless stated otherwise. When reading a supplier's or distributor's 'margin', always check which base is meant.
A Diwali sale at an electronics shop in Indore offers 35% off a mixer grinder marked at ₹2,400. The shop bought it from the distributor for ₹1,450.
Selling price after discount: SP = MP × (1 − d/100) = 2400 × 0.65 = ₹1,560
Profit: SP − CP = 1,560 − 1450 = ₹110
Profit %: 110 ÷ 1450 × 100 = 7.59%
Markup on cost: (2400 − 1450) ÷ 1450 × 100 = 65.52%
Answer: Selling price ₹1,560; Profit ₹110; Markup on cost 65.52%
Calculating profit percentage on selling price instead of cost price.
Applying the discount to cost price instead of marked price.
Assuming a 20% markup and 20% discount cancel out.
Treating margin quoted on selling price as the same as profit on cost.
Ignoring GST and overheads when judging real profitability.
Setting sale discounts that still leave a profit.
Solving profit, loss and discount questions in aptitude exams.
Pricing handmade or resale goods for small businesses.
Checking whether a festival offer is really as generous as it looks.
Is profit percentage on cost or selling price?
On cost price, unless a question says otherwise.
How do I find the discount for a target profit?
Target SP = CP × (1 + profit%), then discount = (MP − SP) ÷ MP × 100.