Profit & Loss: Anchoring Every % to Cost Price
What it is
Profit and loss questions revolve around three numbers — cost price (CP), selling price (SP), and marked price (MP) — and one rule that trips up almost everyone: profit or loss percentage is ALWAYS calculated on the cost price, never on the selling price or the marked price, unless the question explicitly says otherwise.
The core method
Profit% = (SP − CP)/CP × 100, so SP = CP × (1 + profit%/100). When a discount is involved, it is applied to the MARKED price to get the SP: SP = MP × (1 − discount%/100). A mark-up followed by a discount is just two multiplying factors chained together, exactly like a percentage-change problem.
Worked example
A trader marks an article 40% above its cost price, then offers a 15% discount on the marked price. Find his profit percentage.
Let CP = ₹100 (using 100 keeps the arithmetic as direct percentages). Marked price = 100 × 1.40 = ₹140. Selling price after the 15% discount = 140 × 0.85 = ₹119. Profit = SP − CP = 119 − 100 = ₹19. Profit% = (19/100) × 100 = 19%, calculated on the CP of 100 — not on the SP of 119 and not on the MP of 140.
Common traps
- Calculating profit% on the marked price or selling price instead of the cost price — this silently gives a different (wrong) number.
- Adding the mark-up % and discount % directly (40% − 15% = 25%) instead of multiplying the retention factors (1.40 × 0.85 = 1.19, i.e., 19%).
- Forgetting that "discount" is always off the marked price, while "profit/loss %" is always on the cost price — two different anchors in the same problem.
What the exam tests here
Across the 3 papers we hold, this skill was asked 1 time, not every sitting — 1 of 3.
What it actually asked:
- overall gain when part of stock sells at cost (2024)
Worked example 2 — working backwards from selling price
An article sold for ₹840 yields a profit of 20%. At what price must it be sold to yield a profit of 35%?
The 20% is a percentage of cost price, so ₹840 is 120% of CP. CP = 840 / 1.20 = ₹700. The required selling price is 700 × 1.35 = ₹945.
The error the question is built to catch is adding 15% to ₹840 (giving ₹966). That treats the extra 15 points as a percentage of the selling price, which is not what a profit percentage means. Every profit or loss percentage in this topic is anchored to cost price unless the question explicitly says otherwise — recover CP first, always, and the rest is one multiplication.
Speed technique
When an article is sold at two different prices, the difference in selling prices equals the difference in profit percentages applied to the same CP. So if selling at ₹960 gives as much profit as selling at ₹640 gives loss, then CP is exactly the midpoint: (960 + 640)/2 = ₹800. Spotting that symmetry skips two equations.
A quick discount-and-markup chain: marking up by m% and then discounting by d% leaves a net factor of (1 + m/100)(1 − d/100). A shopkeeper who marks up 40% and offers 25% off still makes 1.40 × 0.75 = 1.05, a 5% profit — the classic "appears to lose, actually gains" setup.
Dishonest-weight questions have their own shortcut: gain% = (quantity charged for − quantity actually given) / (quantity actually given) × 100. Handing over 1,000 g while charging for 1,200 g gives 200/1000 = 20%. The classic phrasing is the same formula read the other way — "professes to sell at cost price but uses a 900 g weight for a kg" gives 100/900 = 11.11%, not 10%. The denominator is always what the customer actually received.
Check yourself
- A trader sells two radios at ₹1,200 each, gaining 20% on one and losing 20% on the other. Overall?
Show answer
CPs are 1,000 and 1,500; total CP 2,500 against total SP 2,400 — a loss of ₹100, i.e. 4%. Equal ±r% on equal SPs is always a loss of r²/100 %. - If the cost price of 15 articles equals the selling price of 12, what is the profit percentage?
Show answer
3/12 = 25%. - An item costing ₹450 must sell at a 12% profit after a 10% discount on the marked price. What is the marked price?
Show answer
SP = 504; MP = 504 / 0.90 = ₹560.
Exam framings you will actually see
- "Sold at a loss of 10%; had it sold for ₹X more, the gain would be 15%" — the ₹X spans 25% of CP, so CP = X/0.25 immediately.
- "Marked price, discount and profit together" — three quantities, two relations; write MP, SP and CP as factors of one another and solve in one line.
- "Faulty weight" — gain% is (error / true weight) × 100, computed on the true weight.
- "Overall profit on two items sold at the same price with equal ±r%" — always a net loss of r²/100 percent, whatever the price.
- "Break-even after a discount" — asked as "what maximum discount can be offered while still making x% profit", answered by fixing SP from CP and then solving for the discount off MP.
The constant across all five: recover cost price first. Every profit and loss percentage in the syllabus is a fraction of CP, so a question that hides CP is really asking you to find it.
Try it: Profit & Loss questions
Real questions from the PGCET MBA bank on exactly this skill. Pick an answer to see the full solution — the intuition, the worked steps, the faster methods and the traps.
The marked price of a shirt is ₹500. The shopkeeper offers a discount of 10%. Find the selling price.
Show the answer and worked solution
Answer: option B
Discount is calculated on the marked price, not the cost price: Discount = 10% of 500 = ₹50.
Selling price is what remains after removing the discount: SP = MP − Discount.
Substitute the values: SP = 500 − 50.
That gives SP = ₹450 - option B.
A shopkeeper marks an item at ₹1000 and offers two successive discounts of 20% and 10%. Find the final selling price.
Show the answer and worked solution
Answer: option B
Successive discounts are applied one after another on the reduced price, not added together: SP = MP × (1 − ) × (1 − ).
Substitute MP = 1000: SP = 1000 × 0.8 × 0.9.
That gives SP = ₹720 - option B.
A dealer sells two watches for ₹960 each. On one he gains 20% and on the other he loses 20%. What is his overall result on the two-watch transaction?
Show the answer and worked solution
Answer: option D
Find each cost price from the selling price: CP of the gain watch = = ₹800; CP of the loss watch = = ₹1,200.
Total CP = 800 + 1200 = ₹2,000, and total SP = 960 × 2 = ₹1,920.
Overall result = Total SP − Total CP = 1920 − 2000 = −₹80, i.e. a loss of ₹80, which is option D.
A shopkeeper sells an article for ₹690, making a profit of ₹90. Find his profit percentage.
Show the answer and worked solution
Answer: option C
The cost price is the selling price minus the profit amount: CP = 690 − 90 = ₹600.
Profit percent is always calculated on the cost price: Profit% = (Profit ÷ CP) × 100.
Substitute the values: Profit% = (90 ÷ 600) × 100.
That gives Profit% = 15% - option C.
A sells an item to B at a profit of 20%, and B sells the same item to C at a profit of 25%. If C pays ₹1500 for it, what was A's cost price?
Show the answer and worked solution
Answer: option C
Work backwards from C's price, dividing out each seller's profit margin in turn.
B's cost price = C's price / 1.25 = = ₹1200.
A's cost price = B's cost price / 1.20 = .
= ₹1000, so A's original cost price was ₹1000 — option C.
Answer above — every one shows its working.