Profit, Loss & Discount
Solve every “Comparing Quantities” problem — profit and loss, cost and selling price, discounts, successive discounts, marked price and GST — with the formula and each step in rupees.
Profit = SP − CP and Loss = CP − SP, and both percentages are always worked out on the cost price: Profit % = Profit ÷ CP × 100. If the CP is ₹1,250 and the SP is ₹1,500, the profit is ₹250, so the profit is 20%. Discount is different — it is always calculated on the marked price.
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Step-by-step working
Shop maths, explained
Pick a problem type, enter the prices or percentages from your question, and get the answer in rupees with the formula and full working.
Choose the problem
Profit and loss, finding SP or CP, discounts, successive discounts, marked price or GST.
Enter the numbers
Commas are fine — 1,25,000 works. Toggle profit/loss or add/remove GST as needed.
See the money bars
Bars compare CP, SP and MP so you can see where the profit, loss or discount sits.
Copy the working
Every step shows the formula with your numbers — ideal for checking homework.
Profit and loss
Profit = SP − CP Loss = CP − SP
Profit % = Profit ÷ CP × 100 — profit and loss percentages are always on the cost price.
SP and CP from a percentage
SP = CP × (100 ± p%) ÷ 100
CP = SP × 100 ÷ (100 ± p%) (use + for profit, − for loss).
Discount
Discount is always calculated on the marked price: SP = MP × (100 − d) ÷ 100
Two discounts of a% and b% equal one discount of a + b − ab/100 — so 20% then 10% is 28%, not 30%.
GST
GST is added to the price of goods and services. Inside a state it is split equally into CGST (Centre) and SGST (State); between states one IGST is charged.
Remove GST: Base = Total × 100 ÷ (100 + rate)
Profit, Loss & Discount — your questions
What is the formula for profit and loss percentage?
Profit = SP − CP and Loss = CP − SP. Both percentages are taken on the cost price: Profit % = Profit ÷ CP × 100 and Loss % = Loss ÷ CP × 100. If an article bought for ₹800 sells for ₹920, the profit is ₹120 and the profit percentage is 120 ÷ 800 × 100 = 15%.
How do I find the cost price from the selling price?
Use CP = SP × 100 ÷ (100 ± p%), taking plus for a profit and minus for a loss. If an item sells for ₹1,150 at a 15% profit, then CP = 1150 × 100 ÷ 115 = ₹1,000. Never take 15% of the selling price — percentages in this chapter are always on the cost price.
What is the formula for two successive discounts?
Two discounts of a% and b% are equivalent to a single discount of a + b − ab/100. So 20% followed by 10% is 20 + 10 − 2 = 28%, not 30%, because the second discount applies to the already reduced price. On a marked price of ₹5,000 that means paying ₹3,600, not ₹3,500.
How do I calculate the marked price to allow a discount and still make a profit?
Work out the selling price you need, then raise it to cover the discount. For CP ₹600 with 20% profit wanted and 10% discount given: SP = 600 × 1.20 = ₹720, then MP = 720 × 100 ÷ 90 = ₹800. So marking the item at ₹800 and offering 10% off still leaves the 20% profit.
How do I remove GST from a total amount?
Divide the total by (100 + rate) and multiply by 100: Base = Total × 100 ÷ (100 + rate). A bill of ₹2,950 including 18% GST gives a base price of 2950 × 100 ÷ 118 = ₹2,500, so the GST was ₹450. Dividing by 1.18 gives the same result.
What is the difference between CGST, SGST and IGST?
When goods or services are supplied within a state, the GST is split equally between the Centre and the state, so 18% becomes 9% CGST and 9% SGST. When the supply crosses a state border, a single IGST is charged at the full rate instead. The total tax paid is the same either way.
Is discount calculated on the marked price or the cost price?
Always on the marked price, also called the list price — that is the price printed on the label before any reduction. SP = MP × (100 − d) ÷ 100, so 25% off a marked price of ₹2,400 gives a sale price of ₹1,800. Profit and loss percentages, by contrast, are always on the cost price.