Profit and Loss
Profit and loss questions are percentage problems wearing business language, and the base of every calculation must always be the cost price unless the question says otherwise.
10 questions · 5 minutes · instant scoring
What this topic actually tests
Profit and loss questions rest on two definitions: profit percent = (Selling Price - Cost Price)/Cost Price x 100, and loss percent = (Cost Price - Selling Price)/Cost Price x 100 — in both cases the cost price (CP) is the base, never the selling price (SP), unless a question explicitly asks for a percentage 'on selling price'. When a marked price (MP) and a discount are both involved, work in two clean steps: first find SP by applying the discount to MP, then compare that SP to CP to get the profit or loss percent — do not try to combine markup and discount percentages by simple addition or subtraction, since they act on different bases (MP is the base for discount, CP is the base for profit). A very fast CLAT technique for 'CP of m articles equals SP of n articles' questions is to note that profit percent = (m-n)/n x 100 directly, avoiding a full algebraic setup. Worked example: a trader marks goods 40% above cost price (so MP = 1.40 x CP) and then offers a 10% discount on the marked price. SP = 1.40 x 0.90 x CP = 1.26 x CP, so the profit is 26% of CP — not 40% - 10% = 30%, because the discount is taken on the marked price, not the cost price. For questions involving two articles sold at the same price with one at a percentage gain and the other at an equal percentage loss, there is always a net loss, and it equals (common percentage)^2 / 100 — for a 20%/20% split this gives a net loss of 400/100 = 4%, a shortcut worth memorising since it appears often.
The common trap on this topic
The most damaging trap in profit and loss is silently switching the base between cost price and selling price mid-calculation, especially in markup-and-discount questions where the marked price is a third value distinct from both. Students frequently compute the discount correctly but then compare the resulting selling price to the marked price instead of the cost price when finding profit percent, producing a completely wrong answer even though every individual step looked correct. A second frequent trap is the 'equal gain, equal loss on two items sold at the same price' scenario: because both transactions have the same selling price but different cost prices, the intuitive assumption of 'no net profit or loss' is wrong — there is always a net loss whose magnitude depends only on the common percentage, and the direction (loss, never profit) is easy to forget under time pressure. A third trap involves questions where cost price and selling price are both altered by the same fixed amount (not the same percentage); because a fixed absolute change affects a smaller base more than a larger one in percentage terms, the profit percentage after the change is never a simple shift from the original percentage, and must be recalculated using the new CP and new SP from scratch.
Take the micro-test
A shopkeeper buys an article for Rs 800 and sells it for Rs 960. Find his profit percent.
By selling an article for Rs 810, a man loses 10%. At what price should he sell it instead to gain 10%?
A trader marks his goods 40% above cost price and then allows a discount of 10% on the marked price. Find his profit percent.
What was the dealer's total profit?
What was the dealer's overall profit percent on this transaction?
A man sells two watches at Rs 1,200 each. On one watch he gains 20%, and on the other he loses 20%. Find his overall profit or loss percent on the two transactions.
The cost price of 15 articles equals the selling price of 12 articles. Find the profit percent.
A man sold an article at a loss of 15%. Had he sold it for Rs 300 more, he would have gained 5%. Find the cost price of the article.
A fruit vendor buys oranges at 5 for Rs 10 and sells them at 4 for Rs 10. Find his profit percent.
An article is sold at a profit of 25%. If both the cost price and the selling price had been Rs 20 less, the profit would have been 30%. Find the original cost price.
FAQ
Is profit percent always calculated on cost price?
Yes, unless the question explicitly says "profit on selling price" — the default and far more common convention, including on CLAT, is that profit and loss percentages use cost price as the base.
How do I handle a question that gives both a markup percentage and a discount percentage?
Never subtract the two percentages directly. Convert the markup into the marked price (MP = CP x (1 + markup%)), apply the discount to that marked price to get the selling price, and only then compare the selling price to the cost price to find the actual profit or loss percentage.
What is the shortcut for "sold two items at the same price, one at +x% and one at -x%"?
This situation always produces a net loss, and the loss percentage equals x-squared divided by 100 — for example, a 10% gain and 10% loss on two items sold at equal prices gives a net loss of 1%.
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