📑 On this page
⚡ The short answer
Profit % = (SP − CP) ÷ CP × 100. The base is the cost price, including every rupee spent before the sale. Forward: SP = CP × (1 + p/100). Back: CP = SP ÷ (1 + p/100). The trap: dividing by SP, or taking the percentage of SP to find CP.
🎬 The 30-second story
Aarav's 25% that wasn't
1
“Bought a used phone for ₹8,000, sold it for ₹10,000. ₹2,000 profit, 25%!”
📱
Aarav
Aarav has started flipping phones.
2
“And the ₹800 screen? The ₹200 courier?”
🧾
Zoya
Zoya has seen the receipts.
3
“Fine. ₹1,000 on a ₹10,000 sale. 10%.”
💸
Aarav
He fixes the cost, breaks the base.
4
“Divide by what it cost you, not what they paid.”
🧮
Tara
Tara puts down her chai.
Tara's maths: CP = 8,000 + 800 + 200 = ₹9,000. Profit = ₹1,000. Profit % = 1,000 ÷ 9,000 × 100 = 11.11%. Not 25% (forgotten costs), not 10% (wrong base).
What do cost price, selling price and profit actually mean?
Strip away the jargon and there are two numbers. The cost price (CP) is everything the seller spent to get the item ready to sell. The selling price (SP) is what the buyer hands over. If SP is bigger, the gap is profit; if smaller, loss. The rest is bookkeeping.
🧮 The formula
The only relationship you need
🧾
Cost price
price paid + repairs + transport
+
📈
Profit
negative if it's a loss
=
💰
Selling price
A fest committee that buys T-shirts at ₹250 and pays a printer ₹5,000 has not spent ₹250 a shirt. Every overhead before the sale joins CP. Caselets call it 'expenditure' or 'cost of production'; turnover and revenue mean SP.
📌 One question before every sum
Ask: percentage of what? Profit and loss % sit on CP. Discounts sit on the marked price. A margin, only when the passage says so, sits on SP.
How do you calculate profit percentage, and why is it on cost price?
Profit % answers one question: for every ₹100 I put in, how much came back on top? What you put in is the cost, so cost is the base: Profit % = (SP − CP) ÷ CP × 100. It is simply the percentage change from CP to SP.
🟦 Picture the percent
Same ₹100 profit, two different percentages
On CP: 25%
₹100 profit on a ₹400 cost: right
On SP: 20%
the same ₹100 on a ₹500 sale: the trap option
🎛️ Try it yourself — change any number
Profit % calculator
Profit
1,000
Profit %
11.11%
(10,000 − 9,000) ÷ 9,000 × 100 = +11.11%
Starts on Aarav's phone: 11.11%. Set SP to 8,100 for a 10% loss. Set CP to 8,000 and SP to 10,000: the 25% he thought he made.
Think in multipliers, not in subtractions
A 20% profit means SP = CP × 1.2, or 6/5. A 20% loss means SP = CP × 0.8, or 4/5. See every percentage as a fraction and most questions become one multiplication.
| Profit / loss | SP ÷ CP | To get SP | To get CP |
|---|---|---|---|
| +12.5% | 9/8 | × 1.125 | × 8/9 |
| +20% | 6/5 | × 1.2 | × 5/6 |
| +25% | 5/4 | × 1.25 | × 4/5 |
| +33⅓% | 4/3 | × 4/3 | × 3/4 |
| −20% | 4/5 | × 0.8 | × 5/4 |
| −25% | 3/4 | × 0.75 | × 4/3 |
→ scroll to see more
How do you find the cost price from the selling price?
Going forward you multiply; going back you divide by the same multiplier. The percentage sits on CP, the number you don't know, so you can't take it off SP.
✍️ Worked example
Warm-up
⏱ 30 sec
The cricket bat
Kabir sells a cricket bat for ₹1,380 and makes a 15% profit. What did the bat cost him?
- 115% profit means SP = CP × 1.15.
- 2CP = 1,380 ÷ 1.15 = 1,200.
- 3Check: 1,200 + 15% of 1,200 = 1,200 + 180 = 1,380.
Answer: CP = ₹1,200
⚡ Why ₹1,173 is wrong
The trap answer takes 15% off ₹1,380 and gets ₹1,173. Check by going forward: 1,173 × 1.15 isn't 1,380.
✍️ Worked example
CLAT level
⏱ 45 sec
The loss you want to flip
Rohan sells his old guitar for ₹2,640 and loses 12%. At what price should he have sold it to make an 8% profit?
- 1A 12% loss means 2,640 is 88% of CP, so CP = 2,640 ÷ 0.88 = ₹3,000.
- 2For 8% profit, SP = 3,000 × 1.08 = ₹3,240.
Answer: He should sell for ₹3,240
⚡ The ratio route
Skip CP. The two prices are in the ratio 108 : 88, so SP = 2,640 × 108/88 = 30 × 108 = 3,240.
What is the fastest way to solve profit and loss questions?
Three habits do most of the work. Assume CP = 100 when only percentages are given. Chain multipliers instead of finding every middle value. And when the options are numbers, plug one in.
🧭 Decision flow
Which formula do I need?
❓ Know both CP and SP?
Yes →
Profit % = (SP − CP) ÷ CP × 100
No ↓
❓ Know CP and the %?
Yes →
SP = CP × (100 ± p)/100
No ↓
❓ Know SP and the %?
Yes →
CP = SP × 100/(100 ± p). Divide; never take p% of SP
No ↓
❓ Two selling prices for one item?
Yes →
Ratio of multipliers, or call CP x
No →
Assume CP = 100 and follow the story
✍️ Worked example
Tricky
⏱ 40 sec
Same price, opposite fates
Kabir sells two speakers for ₹2,400 each, one at 20% profit, the other at 20% loss. Net result?
- 1Speaker 1: CP = 2,400 ÷ 1.2 = ₹2,000. Speaker 2: CP = 2,400 ÷ 0.8 = ₹3,000.
- 2Total CP = ₹5,000; total SP = ₹4,800. Loss = ₹200.
- 3Loss % = 200 ÷ 5,000 × 100 = 4%.
Answer: A net loss of 4%, not break-even
⚡ The p²/100 rule
Same SP, ±p%: always a loss of p²/100 %. Here 20² ÷ 100 = 4%.
How does profit and loss hide inside a CLAT caselet?
Since 2020, CLAT gives a company paragraph instead: total production, total turnover, and each product's share of both. Turnover is SP. Cost arrives inside the question as a cost per tonne. Build the table before you read an option.
📊 The data
CLAT 2022 caselet: each product's share of production vs turnover
Share of productionShare of turnover
P
21%
18%
Q
16%
17%
R
18%
20%
S
20%
25%
T
25%
20%
Total: 3,000 tonnes, ₹50 million. Gold above blue means the product sells above the average ₹16,666.67 a tonne.
| Product | Tonnes | Turnover (₹ million) | Price per tonne (₹) |
|---|---|---|---|
| P | 630 | 9 | 14,285.71 |
| Q | 480 | 8.5 | 17,708.33 |
| R | 540 | 10 | 18,518.52 |
| S | 600 | 12.5 | 20,833.33 |
| T | 750 | 10 | 13,333.33 |
→ scroll to see more
💡 Estimate before you calculate
R costs ₹15,000 a tonne and sells for about ₹18,500: a bit over 23%. T costs ₹20,000 and sells for about ₹13,300: clearly a loss. Know the answer's shape before you calculate.
Which profit and loss traps does CLAT set?
⚔️ Side by side
Mark-up vs margin: the same rupees, two percentages
🧾Mark-up (on CP)
profit ÷ cost price
- •CLAT's default
- •₹80 cost, ₹100 sale: 25%
🏷️Margin (on SP)
profit ÷ selling price
- •Only if the passage says 'on SP'
- •₹80 cost, ₹100 sale: 20%
VS
| Test | Mark-up (on CP) | Margin (on SP) |
|---|---|---|
| Convert | markup p → margin p/(100 + p) | margin m → markup m/(100 − m) |
| 25% ↔ 20% | 25/125 = 20% | 20/80 = 25% |
A café that wants a 25% margin must mark up by 33⅓%.
Overall profit % is not the average of the two percentages
Zoya sells a ₹1,000 bag at 10% profit and a ₹3,000 jacket at 30%. Up 20%? No: CP ₹4,000, SP 1,100 + 3,900 = ₹5,000, so 25%. Overall profit % is a weighted average by CP. Only equal CPs allow a simple average, and CLAT 2019 used exactly that.
How has CLAT asked profit and loss?
📝 Asked in CLAT 2022
· Q141
Profit % from a caselet
… Company produces five products namely P, Q, R, S and T. Total production of the company for the financial year 2021-22 is 3,000 tonnes and the turnover of the company is ₹50 million. … 'R' accounts for 18% of the total production and 20% of the turnover; 'S' accounts for 20% of the total production and 25% of the turnover, and; 'T' accounts for 25% of total production and 20% of turnover.
What is the percentage of profit earned from sale of R, if the expenditure incurred on production of 'R' is ₹15,000/- per tonne?
A20%
B23.46%
C26.55%
D25%
Reveal answer + reasoning
Answer: B
Build the R row. Production = 18% of 3,000 = 540 tonnes. Turnover (SP) = 20% of ₹50 million = ₹10 million. Cost (CP) = 540 × 15,000 = ₹8.1 million. Profit ₹1.9 million ÷ 8.1 × 100 = 23.46%. Estimate: just under a quarter. About 75 seconds.
Why the others fail
- A — R's turnover share, lifted from the passage.
- C — No sensible base gives it; profit on SP is only 19%.
- D — S's turnover share; the estimate says just under 25%.
📝 Asked in CLAT 2022
· Q143
Loss from a caselet
(Same passage.) Total production 3,000 tonnes; turnover ₹50 million. 'T' accounts for 25% of total production and 20% of turnover.
How much loss is incurred to company, if the expenditure on production of 'T' was ₹20,000 per tonne?
A5 million
B10 million
C4 million
D7 million
Reveal answer + reasoning
Answer: A
T's production = 25% of 3,000 = 750 tonnes. Cost = 750 × 20,000 = ₹15 million. Turnover = 20% of 50 = ₹10 million. Loss = 15 − 10 = ₹5 million. About 45 seconds.
Why the others fail
- B — That's T's turnover (SP), not the loss.
- C — No consistent base gives it.
- D — Unsupported: 15 − 10 can only be 5.
📝 Asked in CLAT 2019
· Q46
Two selling scenarios
A book seller sold a box of 10 pencils for Rs. 80 and incurred a loss. Had he sold it for Rs. 98, his gain would have been twice the loss he incurred earlier.
The cost price of the box of pencils is:
ARs. 84
BRs. 86
CRs. 88
DRs. 90
Reveal answer + reasoning
Answer: B
Our solution (2019 has no official key). Let CP = x. Loss at ₹80 = x − 80; gain at ₹98 = 98 − x. Gain = 2 × loss: 98 − x = 2x − 160, so 3x = 258 and x = 86. Check: loss 6, gain 12. The '10 pencils' is decoration. About 40 seconds.
Why the others fail
- A — Loss 4, gain 14: not twice.
- C — Loss 8, gain 10: not twice.
- D — Gain 8 is smaller than loss 10.
📝 Asked in CLAT 2019
· Q58
Overall profit on two items
Naresh bought a bicycle each for his two sons, each bicycle priced at Rs. 3500. If the first bicycle is sold at a profit of 5%,
then how much should the other bicycle be sold for, to gain a total of 20% on both?
A15%
B10%
C25%
D35%
Reveal answer + reasoning
Answer: D
Our solution (2019 has no official key). The options are percentages, so read 'how much' as the profit % on the second bicycle. Total CP ₹7,000 needs SP ₹8,400. The first fetches 3,500 × 1.05 = ₹3,675, so the second needs ₹4,725: 1,225 on 3,500 = 35%. Fast: equal CPs, so (5 + x) ÷ 2 = 20 and x = 35. About 30 seconds.
Why the others fail
- A — 20 − 5: gives only 10% overall.
- B — Gives only 7.5% overall.
- C — 20 + 5. The first is 15 points below 20%, so the second must be 15 above.
Can you beat these profit and loss myths and questions?
💥 Myth vs fact
Myth vs fact
🙅 Myth
Profit % can be worked out on whichever price is handy.
Tap to bust it →
✅ Fact
It's on CP unless the passage says otherwise: ₹100 on a ₹400 cost is 25%, not 20%.
🙅 Myth
To find CP from a 20% profit, take 20% off the SP.
Tap to bust it →
✅ Fact
Divide by 1.2. 20% off ₹1,200 is ₹960; the real CP is ₹1,000.
🙅 Myth
Same price, 20% profit on one and 20% loss on the other, breaks even.
Tap to bust it →
✅ Fact
It's always a loss, of p²/100 %. Here, 4%.
🙅 Myth
Overall profit % is the average of the individual profit %s.
Tap to bust it →
✅ Fact
Only with equal CPs. Otherwise weight by CP: 10% on ₹1,000 and 30% on ₹3,000 is 25%.
🎯 Quick quiz
Five quick ones before the drill
0 / 5
Meher buys phone covers at ₹160 and sells them at ₹200.
Q1. What is her profit %?
₹40 on a cost of ₹160 = 25%. A divides by SP.A helmet is sold for ₹1,170 at a 10% loss.
Q2. What was its cost price?
SP is 90% of CP: 1,170 ÷ 0.9 = ₹1,300. A and C work on SP, the wrong base.The cost price of 15 pens equals the selling price of 12 pens.
Q3. What is the profit %?
Let a pen cost ₹1. 12 pens sell for ₹15: profit 3 on cost 12 = 25%.A café owner wants 25% profit on the selling price.
Q4. By what % must she mark up over cost?
SP = 100: profit 25, cost 75. Mark-up = 25 ÷ 75 = 33.33%.A fest committee buys 200 T-shirts at ₹250 each and pays ₹5,000 for printing. It sells 150 at ₹400 and the other 50 at ₹200.
Q5. What is the committee's profit %?
CP = ₹55,000; SP = ₹70,000; 15,000 ÷ 55,000 = 27.27%. A divides by SP; C and D leave printing out.🎯 Profit and loss in a nutshell
- CP is everything spent before the sale; SP is what the buyer pays.
- Profit and loss % are on CP unless the passage says SP.
- Forward multiply by (1 ± p/100); back, divide by it.
- Same SP, p% gain and p% loss: a loss of p²/100 %.
- In a caselet, turnover is SP and expenditure is CP.
📎 Formula card
- Profit = SP − CP; Profit % = Profit ÷ CP × 100
- SP = CP × (100 ± p)/100; CP = SP × 100/(100 ± p)
- Margin m on SP = mark-up m/(100 − m) × 100 on CP
- CP of x items = SP of y items → Profit % = (x − y)/y × 100
- False weight: Profit % = (true − false)/false × 100
- Same SP, ±p% → net loss of p²/100 %
Make the base automatic
Timed profit, interest and speed questions, every answer explained.
Frequently asked questions
What is the formula for profit percentage?
Profit % = (Selling price − Cost price) ÷ Cost price × 100. Cost is the base because it is what you invested. Buy at ₹400, sell at ₹500: ₹100 profit is 25% of cost. Dividing by SP gives 20%, a favourite wrong option.
How do you find cost price when selling price and profit % are given?
Divide: CP = SP × 100 ÷ (100 + profit %). A bat sold for ₹1,380 at 15% profit cost 1,380 ÷ 1.15 = ₹1,200. Taking 15% off ₹1,380 gives ₹1,173, which is wrong because the percentage belongs to cost.
Is profit calculated on cost price or selling price?
On cost price, by default. Divide by SP only when a passage clearly says 'on selling price' or 'margin'. A margin of m% on SP equals a mark-up of m ÷ (100 − m) × 100 on CP, so a 20% margin is a 25% mark-up.
What happens if two items sell at the same price, one at a gain and one at a loss of the same %?
Always a net loss of p² ÷ 100 per cent. Two speakers at ₹2,400 each, one at 20% gain and one at 20% loss, cost ₹2,000 and ₹3,000. Sales of ₹4,800 against costs of ₹5,000 is a 4% loss.
How are profit and loss questions asked in CLAT now?
Mostly inside caselets. A paragraph gives production and turnover with each product's share; the question adds a cost per unit. Find the product's revenue (SP) and total cost (CP), then the gap. CLAT 2022 asked for R's profit % and T's loss this way.
How do you find the overall profit percentage on two items?
Add the costs, add the selling prices, and find profit on total cost. It is not the average of the two percentages unless the costs are equal. A ₹1,000 bag at 10% and a ₹3,000 jacket at 30% give 25% overall, not 20%.
Keep going
📚
Part of the chapter
Profit, Interest & Time-Speed-Work for CLAT Quantitative Techniques
See how this topic fits the whole of Profit, Interest & Time-Speed-Work →
Connected topics in other chapters
Marked Price and Discount
The next layer: a third price, the tag, and a discount taken on it, not on cost.
Cost, Revenue and Per-Unit Price in Caselets
The same CP and SP, scaled up to tonnes and turnover inside a data passage.
Reverse Percentage: Finding the Original Number
Finding CP from SP is a reverse-percentage question wearing a shopkeeper's apron.
Weighted Average
Why the overall profit % on two items is weighted by their cost prices.
Percentage Increase, Decrease and '% More Than'
Profit % is just the percentage change from CP to SP.
Every topic in Profit, Interest & Time-Speed-Work
- 1.Profit and Loss: CP, SP and Profit % (you're here)
- 2.Marked Price and Discount: Mark-up, Sale Price and Profit
- 3.Successive Discounts and Discount Schemes: the Single Equivalent Discount
- 4.Cost, Revenue and Per-Unit Price in Caselets
- 5.Simple Interest: Formula, Shortcuts and CLAT Traps
- 6.Compound Interest and the SI–CI Difference
- 7.Speed, Distance and Time
- 8.Trains, Races and Relative Speed
- 9.Time and Work: the LCM Method
- 10.Pipes and Cisterns