Profit and loss
Buy a bicycle, spend a little getting it repaired, then sell it on — did that turn out well? Profit and loss is the arithmetic that answers exactly that question, for any transaction where an article is bought at one price and sold at another. It sits inside the ICSE Class 8 chapter "Profit, Loss and Discount," building directly on the earlier percentage chapter: once you can express one number as a percentage of another, you can express a profit or a loss as a percentage of the Cost Price. The idea is simple but the bookkeeping has traps — overhead expenses like repair or transport cost must be folded into the Cost Price before anything else is calculated, and profit or loss percentage is always measured against the Cost Price, never the Selling Price. This article restates the core formulas, works through the arithmetic in both directions — amounts to percentages, and percentages back to amounts — and flags the mistakes that cost the most marks.
Profit or loss is the gap between Selling Price and Cost Price (after adding any overheads to CP), and it is always expressed as a percentage of the Cost Price.
The core idea
Every profit-and-loss problem runs on three quantities: the Cost Price (CP), what the article was bought or made for; the Selling Price (SP), what it was sold for; and any overheads — repair, transport, or labour cost incurred between buying and selling. Overheads are always added to CP first, giving an "effective CP," before any profit or loss is worked out. Once SP and the effective CP are known, comparing them tells the story. If , the transaction made a profit; if , it made a loss.
where: is the Selling Price, is the effective Cost Price (original CP plus overheads). Only one of Profit or Loss applies to a given transaction, decided by whether SP or CP is larger. The profit or loss amount by itself doesn't say much — selling a car for ₹5,000 more than it cost is a very different story from selling a pencil for ₹5,000 more than it cost. So profit and loss are always converted to a percentage, and the percentage is always taken of the Cost Price:
where: the denominator in both formulas is CP, never SP — this is the single most important rule in the whole chapter, and it is where most marks are lost. A useful way to picture this: think of CP as always being "100%" of the transaction. A profit stretches SP a bit past 100% of CP; a loss shrinks SP to a bit below 100% of CP. A 20% profit means SP is 120% of CP; a 20% loss means SP is only 80% of CP. Framing it this way is exactly the "percentage of a base quantity" skill from the earlier Percent and Percentage chapter, now applied to buying and selling.
The same two formulas can be rearranged to run backwards — finding SP when CP and a profit or loss percentage are known, or finding CP when SP and a percentage are known:
where: the fraction is always built from "100 plus or minus the percentage" — plus for a profit (SP is bigger than CP), minus for a loss (SP is smaller than CP). To go from CP to SP, multiply by that fraction; to go from SP back to CP, divide by it.
The goal is to take three raw numbers — an original purchase price, an overhead expense incurred before resale, and the price the article was actually sold for — and turn them into a single profit percentage that is measured correctly against the true (effective) cost of the transaction, not against the original purchase price alone and not against the selling price.
Step 1. Combine the original CP with the overheads to get the effective CP, since every rupee spent before the sale is part of the true cost of the transaction: .
Step 2. Compare SP with this effective CP to decide whether the transaction is a profit or a loss, and find the amount: if , ; if , .
Step 3. Convert that amount to a percentage by dividing by the effective CP, never by SP, and multiplying by 100: (or the equivalent loss version). This last division is exactly why Step 1 mattered — using the wrong CP here throws off the whole answer even if Steps 1 and 2 were done correctly.
Worked example
A shopkeeper buys a bicycle for ₹4,200 and spends ₹300 repairing it, then sells it for ₹4,950. Find his profit or loss percent. Then suppose instead he had sold it for ₹4,050 at a loss of exactly 10% — find that Selling Price directly from the loss percentage, to check the reverse direction of the formula.
Step 1. Find the effective CP. .
Step 2. Compare with the actual SP of ₹4,950. Since , this is a profit: .
Step 3. Convert to a percentage using CP as the base: . The shopkeeper made a 10% profit.
Step 4. Now check the reverse direction. If instead he had sold at a 10% loss on the same effective CP of ₹4,500, the Selling Price would be , matching the number given in the question. This confirms the formula works both ways: 10% profit gave SP = ₹4,950; 10% loss on the same CP would have given SP = ₹4,050.
Common traps
- Using SP instead of CP as the base for the percentage. Profit% and Loss% are always calculated on CP — dividing by SP instead gives a wrong percentage even when the profit or loss amount itself is right.
- Forgetting to add overheads to CP before comparing with SP. Repair, transport, or labour cost is part of the true cost and must be folded into CP first, not subtracted from the final profit separately.
- Sign confusion between Profit and Loss. Writing "Loss = SP − CP" gives a negative number; always subtract the smaller from the larger and let the situation (SP > CP or CP > SP) decide which one it is.
- Dividing instead of multiplying when going from CP to SP. With a known profit%, SP is the larger fraction of CP — multiply by , don't divide.
Ask the tutor: Want to try a profit-and-loss word problem with multiple overhead items, or double-check whether you're supposed to add or divide in a tricky question — ask the AI tutor to walk through it with you step by step.
Why is profit or loss percent always calculated on CP and never on SP?
Because CP is the fixed reference point of the transaction — it's what was actually paid, before any outcome is known. SP changes depending on how the sale went, so using it as the base would make the "percentage" mean something different in every problem. CP as the base lets you compare deals fairly: a 10% profit always means the same thing, SP is 110% of whatever was paid, regardless of the actual rupee amounts involved.
Do overheads get added to CP even if they happen after the sale, like delivery to the buyer?
No — the rule is about when the expense happens relative to getting the article ready to sell, not literally before or after the sale date. Repair, transport to your own shop, or labour to prepare the article for sale are added to CP because they were necessary to bring the article to a sellable state. If an expense is charged separately to the buyer after the sale (like delivery they pay for), it is usually kept out of the CP/SP calculation entirely unless a question states otherwise — always follow exactly what the word problem says was paid by whom.
How do I tell quickly whether a percentage question wants me to multiply or divide by 100 plus or minus the percent?
Ask which quantity you already have. If you have CP and want SP, you're moving from the fixed 100% base outward to the profit/loss point, so you multiply CP by . If you have SP and want CP, you're moving backward from that point to the 100% base, so you divide SP by the same fraction (or equivalently multiply by its reciprocal). A quick sanity check: for a profit, SP must come out bigger than CP; for a loss, SP must come out smaller than CP — if your answer doesn't satisfy that, you used the wrong operation.