A Shop Can Give a Discount and Still Make a Profit
Learn to include overheads in cost price, calculate profit or loss percent, find the selling price from the cost price and back again, and work out discount, marked price and the profit left after it.
How can a shop cut the price and still earn a profit?
Because the discount is taken off the marked price, not off the cost price. A shirt bought for ₹850 and marked ₹1200 still sells for ₹1020 after a 15 percent discount — a profit of ₹170.
The marked price is deliberately set high enough to absorb the cut. This page covers everything in the ICSE Class 7 Mathematics chapter on profit and loss: cost price with overheads, profit and loss percent, finding the selling and cost prices, and discount.
The marked price is deliberately set high enough to absorb the cut. This page covers everything in the ICSE Class 7 Mathematics chapter on profit and loss: cost price with overheads, profit and loss percent, finding the selling and cost prices, and discount.
Formula
How do you calculate profit or loss as a percentage?
The cost price (CP) is what the seller paid, plus any overheads — transport, repairs, labour and packing. The selling price (SP) is what the buyer pays.
Both percentages are always taken on the cost price:
Worked example. A trader buys goods for ₹450 and spends ₹50 on transport, then sells them for ₹575.
Total — the overheads are part of the cost price.
A loss example. A cycle bought for ₹4000 is sold for ₹3600:
The two errors to avoid are both about the base. Overheads must be added to the cost price before anything else, and the percentage is taken on the cost price — never on the selling price. Dividing the ₹75 profit by ₹575 would give 13.04 percent, which is wrong.
Both percentages are always taken on the cost price:
Worked example. A trader buys goods for ₹450 and spends ₹50 on transport, then sells them for ₹575.
Total — the overheads are part of the cost price.
A loss example. A cycle bought for ₹4000 is sold for ₹3600:
The two errors to avoid are both about the base. Overheads must be added to the cost price before anything else, and the percentage is taken on the cost price — never on the selling price. Dividing the ₹75 profit by ₹575 would give 13.04 percent, which is wrong.
How do you find the selling price from the cost price?
Treat the cost price as 100 and scale it.
Worked example, profit. An article costing ₹800 is sold at 12 percent profit:
Worked example, loss. An article costing ₹1500 is sold at 8 percent loss:
Worked example with overheads. A dealer buys a fan for ₹1200, spends ₹100 on repairs, and wants a 20 percent profit. The total CP is ₹1300, so
A vegetable seller pricing produce does this every morning, adding a margin onto what the wholesale market charged.
The size check is immediate and worth using. A profit must give an SP above the CP, and a loss an SP below it — so ₹896 above ₹800 and ₹1380 below ₹1500 are both plausible, while the reverse would signal that 112 and 92 had been swapped.
Worked example, profit. An article costing ₹800 is sold at 12 percent profit:
Worked example, loss. An article costing ₹1500 is sold at 8 percent loss:
Worked example with overheads. A dealer buys a fan for ₹1200, spends ₹100 on repairs, and wants a 20 percent profit. The total CP is ₹1300, so
A vegetable seller pricing produce does this every morning, adding a margin onto what the wholesale market charged.
The size check is immediate and worth using. A profit must give an SP above the CP, and a loss an SP below it — so ₹896 above ₹800 and ₹1380 below ₹1500 are both plausible, while the reverse would signal that 112 and 92 had been swapped.
How do you find the cost price from the selling price?
Reverse the last formula. The selling price is of the cost price, so
Worked example, profit. An article sold for ₹960 gave a 20 percent profit:
Check: 20 percent of ₹800 is ₹160, and . Correct.
Worked example, loss. An article sold for ₹680 gave a 15 percent loss:
Check: 15 percent of ₹800 is ₹120, and . Correct.
The tempting shortcut is wrong, and this is where most marks in the chapter are lost. Taking 20 percent off ₹960 gives ₹768, not ₹800 — because the 20 percent was a percentage of the cost price, not of the selling price. The selling price is 120 percent of the cost, so you must divide by 120 and multiply by 100.
Always verify by working forwards from your answer, as above. That one line catches the error every time.
Worked example, profit. An article sold for ₹960 gave a 20 percent profit:
Check: 20 percent of ₹800 is ₹160, and . Correct.
Worked example, loss. An article sold for ₹680 gave a 15 percent loss:
Check: 15 percent of ₹800 is ₹120, and . Correct.
The tempting shortcut is wrong, and this is where most marks in the chapter are lost. Taking 20 percent off ₹960 gives ₹768, not ₹800 — because the 20 percent was a percentage of the cost price, not of the selling price. The selling price is 120 percent of the cost, so you must divide by 120 and multiply by 100.
Always verify by working forwards from your answer, as above. That one line catches the error every time.
How do you calculate discount and the profit left after it?
The marked price (MP) — also called the list price or printed price — is the price displayed before any reduction. The discount is a reduction on the marked price.
Worked example. A shirt is marked ₹1200 with a 15 percent discount:
Profit after a discount. The shopkeeper's cost price was ₹850, so
That is the opening question answered in full — a 15 percent discount still left a 20 percent profit.
Finding the marked price. An article sold for ₹1020 after a 15 percent discount had a marked price of
The distinction that must stay sharp is the base of each percentage. Discount percent is on the marked price; profit percent is on the cost price. In this example the two bases were ₹1200 and ₹850, so the 15 percent and the 20 percent are not comparable figures at all — which is exactly how a discounted sale remains profitable.
Worked example. A shirt is marked ₹1200 with a 15 percent discount:
Profit after a discount. The shopkeeper's cost price was ₹850, so
That is the opening question answered in full — a 15 percent discount still left a 20 percent profit.
Finding the marked price. An article sold for ₹1020 after a 15 percent discount had a marked price of
The distinction that must stay sharp is the base of each percentage. Discount percent is on the marked price; profit percent is on the cost price. In this example the two bases were ₹1200 and ₹850, so the 15 percent and the 20 percent are not comparable figures at all — which is exactly how a discounted sale remains profitable.
Exam tip
Exam tip: writing down which base each percentage uses
Three prices and two percentages make this chapter easy to muddle, so label everything.
Write CP, SP and MP with their values at the top of your working, and add overheads into the CP immediately.
State the base beside each percentage: profit percent is on CP; discount percent is on MP. Mixing the two is the single biggest source of lost marks.
When finding CP from SP, **divide by and multiply by 100 — never subtract the percentage from the selling price.
Verify forwards** in one line: from your CP, apply the profit percent and confirm you get the given SP back.
And end with the rupee sign and a plain statement — cost price = ₹800, profit = 20 percent — rather than a bare number.
Write CP, SP and MP with their values at the top of your working, and add overheads into the CP immediately.
State the base beside each percentage: profit percent is on CP; discount percent is on MP. Mixing the two is the single biggest source of lost marks.
When finding CP from SP, **divide by and multiply by 100 — never subtract the percentage from the selling price.
Verify forwards** in one line: from your CP, apply the profit percent and confirm you get the given SP back.
And end with the rupee sign and a plain statement — cost price = ₹800, profit = 20 percent — rather than a bare number.
Did you know
Why does taking 20 percent off the selling price give the wrong cost price?
Because the 20 percent was never a share of the selling price — it was a share of the cost price.
With a CP of ₹800, the profit of 20 percent is ₹160 and the SP is ₹960. Viewed from the selling price, that ₹160 is only percent of it.
So removing 20 percent of ₹960 removes ₹192 — too much — and lands at ₹768. The correct move is to recognise ₹960 as 120 percent of the cost price, and divide accordingly.
With a CP of ₹800, the profit of 20 percent is ₹160 and the SP is ₹960. Viewed from the selling price, that ₹160 is only percent of it.
So removing 20 percent of ₹960 removes ₹192 — too much — and lands at ₹768. The correct move is to recognise ₹960 as 120 percent of the cost price, and divide accordingly.
Key takeaways
Profit, loss and discount: quick revision
- Overheads are part of the cost price, so CP = purchase price + expenses.
- and — always on the cost price.
- , or for a loss.
- — never subtract the percentage from the SP, since ₹960 at 20 percent profit gives a CP of ₹800, not ₹768.
- Discount is on the marked price: , so ₹1200 less 15 percent is ₹1020.
- A discount can still leave a profit — CP ₹850 against that SP of ₹1020 is a 20 percent profit, because the two percentages use different bases.
You will remember all of this far better after answering five questions on it than after reading it twice.
- and — always on the cost price.
- , or for a loss.
- — never subtract the percentage from the SP, since ₹960 at 20 percent profit gives a CP of ₹800, not ₹768.
- Discount is on the marked price: , so ₹1200 less 15 percent is ₹1020.
- A discount can still leave a profit — CP ₹850 against that SP of ₹1020 is a 20 percent profit, because the two percentages use different bases.
You will remember all of this far better after answering five questions on it than after reading it twice.