📑 On this page
⚡ The short answer
A discount is always taken on the marked price (the tag); profit is always measured on the cost price. Chain them as multipliers: SP = CP × (1 + m/100) × (1 − d/100). The trap: 40% up then 40% off is a 16% loss, not break-even, because the bases differ.
🎬 The 30-second story
The 40% sneaker sale
1
“Bought these for ₹2,500. Tag says ₹3,500. That's 40% up.”
👟
Kabir
Kabir stocks new sneakers.
2
“Banner: FLAT 40% OFF. Up 40, down 40. I lose nothing.”
🏷️
Kabir
He thinks the two forties cancel.
3
“40% of ₹3,500 is ₹1,400. You'll sell at ₹2,100. That's below cost!”
🧾
Zoya
Zoya does the maths at the counter.
4
“So every pair loses me money?”
📉
Kabir
Forty pairs later, he is ₹16,000 poorer.
Tara's maths: The mark-up was 40% of ₹2,500; the discount was 40% of the bigger ₹3,500. Same percentage, bigger base, so the discount wins. ₹2,500 × 1.4 × 0.6 = ₹2,100: a ₹400 loss, i.e. 16% on cost.
What is marked price, and what does a discount mean?
Every shop question has three prices. The cost price (CP) is what the seller paid. The marked price (MP), or list price, is the number on the tag. The selling price (SP) is what you pay at the counter. The discount is the gap between tag and bill: Discount = MP − SP.
Two percentages hang off these prices. The mark-up is how far the tag sits above cost, so it is a percentage of CP. The discount is how far the bill sits below the tag, so it is a percentage of MP. Mix up the bases and everything after is wrong.
⚔️ Side by side
Mark-up vs discount: same % sign, different base
⬆️Mark-up
Cost price → tag
- •Measured on CP
- •(MP − CP) ÷ CP × 100
- •The seller's decision
🏷️Discount
Tag → bill
- •Measured on MP
- •(MP − SP) ÷ MP × 100
- •What the banner shows
VS
| Test | Mark-up | Discount |
|---|---|---|
| Base | Cost price | Marked price |
| Kabir's sneakers | 40% of ₹2,500 = ₹1,000 | 40% of ₹3,500 = ₹1,400 |
The percentages match; the rupees don't. That gap is Kabir's ₹400 loss.
Why is discount taken on marked price and profit on cost price?
Think about who is speaking. The customer only sees the tag, so '25% off' means 25% off what is printed. The shopkeeper's accounts care about what the stock cost, so profit is judged against CP. Each percentage uses the number its speaker actually knows.
🕒 Timeline
One pair of sneakers, three prices
-
1
Cost priceKabir buys at ₹2,500The base for profit or loss.
-
2
Mark-up 40% on CPTag reads ₹3,500₹2,500 × 1.4
-
3
Discount 40% on MPBill comes to ₹2,100₹3,500 × 0.6. The base has grown.
-
4
Result on CPLoss of ₹400 = 16%₹400 ÷ ₹2,500 × 100
The base changes twice: CP, then MP, then back to CP for the verdict. Track that and there is nothing left to memorise.
What is the formula for selling price after a discount?
🧮 The formula
The multiplier chain
📦
CP
seller paid
×
⬆️
(1 + m/100)
mark-up m% on CP
×
🏷️
(1 − d/100)
discount d% on MP
=
🧾
SP
buyer pays
The first two terms multiply to MP.
| You want | Formula | ₹2,500 sneakers |
|---|---|---|
| Selling price | MP × (1 − d/100) | 3,500 × 0.6 = ₹2,100 |
| Discount % | (MP − SP) ÷ MP × 100 | 1,400 ÷ 3,500 = 40% |
| Marked price from SP | SP ÷ (1 − d/100) | 2,100 ÷ 0.6 = ₹3,500 |
| Profit / loss % | (SP − CP) ÷ CP × 100 | −400 ÷ 2,500 = −16% |
→ scroll to see more
⚠️ Going backwards? Divide, never add
Paid ₹2,100 after 40% off? The tag was 2,100 ÷ 0.6 = ₹3,500, not 2,100 + 40% = ₹2,940. The 40% sat on the tag, the very number you are hunting, so undo it by dividing.
How do you solve marked price and discount questions step by step?
✍️ Worked example
Warm-up
⏱ 20 sec
Find the bill
Meher spots a hoodie tagged ₹1,250 with 16% off. What does she pay?
- 116% of ₹1,250 = ₹200 off the tag.
- 2Bill = 1,250 − 200 = ₹1,050.
Answer: ₹1,050, a saving of ₹200.
⚡ The exam-hall shortcut
16% off means you pay 84%: 1,250 × 0.84 = ₹1,050 in one step.
✍️ Worked example
CLAT level
⏱ 40 sec
Mark-up plus discount: profit or loss?
A fest merch seller buys jerseys for ₹1,800, tags them 35% above cost, then gives 20% off. Profit %?
- 1MP = 1,800 × 1.35 = ₹2,430.
- 2SP = 2,430 × 0.8 = ₹1,944.
- 3Profit = ₹144, and 144 ÷ 1,800 × 100 = 8%.
Answer: 8% profit, not 15% (35 − 20).
⚡ The exam-hall shortcut
m − d − md/100 = 35 − 20 − 7 = 8%. You never needed the ₹1,800.
✍️ Worked example
CLAT level
⏱ 45 sec
Work back to the tag
Aarav pays ₹1,530 for headphones after 15% off. The shop bought them for ₹1,200. Find the marked price and the shop's profit %.
- 1He paid 85% of the tag: MP = 1,530 ÷ 0.85 = ₹1,800.
- 2Profit = 1,530 − 1,200 = ₹330.
- 3330 ÷ 1,200 × 100 = 27.5%.
Answer: MP ₹1,800; profit 27.5%.
⚡ The exam-hall shortcut
Dividing by 0.85 is ugly, so test options: 15% of 1,800 is 270, and 1,800 − 270 = 1,530.
✍️ Worked example
Tricky
⏱ 50 sec
How high should the tag be?
A shopkeeper wants to give 10% off and still make 17% profit. By what % above cost must he mark?
- 1Take CP = ₹100, so target SP = ₹117.
- 2SP is 90% of MP: MP = 117 ÷ 0.9 = ₹130.
- 3₹130 on a ₹100 cost is a 30% mark-up.
Answer: 30%, not 27% (17 + 10).
⚡ The exam-hall shortcut
Mark-up = (p + d) ÷ (100 − d) × 100 = 27 ÷ 90 × 100 = 30%. The (100 − d) is why adding always undershoots.
🎛️ Try it yourself — change any number
Kabir's sneaker sale, live
Marked price
3,500
Selling price
2,100
Profit / loss %
−16%
2,500 × 1.4 × 0.6 = 2,100
It opens on Kabir's mistake: a 16% loss. Try 60% up with 25% off (exactly 20% profit). Then set both to 10, 20 and 50 and watch the loss grow as m²/100.
What is the fastest way to solve mark-up and discount questions?
Mark-up then discount is just two successive changes, +m% then −d%, so the successive change rule applies with d entered as negative. Five shortcuts cover nearly every question.
🧩 At a glance
Five exam-hall shortcuts
➗Net profit %
m − d − md/100. 40 up, 40 off: −16%.
🎯Mark-up needed
(p + d) ÷ (100 − d) × 100. 20% profit after 25% off: 60%.
⚖️Equal m and d
Always a loss of m²/100 %. 20 and 20: 4% loss.
🎁Buy x, get y free
Discount = y ÷ (x + y). Buy 3 get 1: 25%.
🔁Same SP, two discounts
MP₁ : MP₂ = (100 − d₂) : (100 − d₁). Bigger discount, bigger tag.
🟦 Picture the percent
'Free' items are discounts in disguise
Buy 3, get 1
You payFree = 25% off
Buy 4, get 1
You payFree = 20% off
Divide the free items by the total you take home. Buy 2 get 1 is 1/3 ≈ 33.3% off, not 50%.
💡 Estimate before you multiply
Mark-up then discount always lands below m − d, by md/100. So 35% up and 20% off must be under 15%: with options 8%, 12%, 15% and 18%, kill the last two before any arithmetic.
Two discounts stacked on one tag (30% then 20% more) work the same way: 0.7 × 0.8 = 0.56, a single 44% off, not 50%. The full playbook is on successive discounts and discount schemes.
How does discount hide in a CLAT caselet?
CLAT now hides discount in a data paragraph: A college fest merch stall bought hoodies at ₹600, T-shirts at ₹250, caps at ₹150 and tote bags at ₹120. It tagged them at ₹900, ₹400, ₹240 and ₹180, and gave 20%, 25%, 30% and 40% off respectively. Turn it into a picture first.
📊 The data
Fest stall: cost, tag and fest-day price
Cost priceMarked priceSelling price
Hoodie · 20% off, profit 20%
₹600
₹900
₹720
T-shirt · 25% off, profit 20%
₹250
₹400
₹300
Cap · 30% off, profit 12%
₹150
₹240
₹168
Tote bag · 40% off, loss 10%
₹120
₹180
₹108
Only the tote bag's selling price falls below its cost.
Read it the way CLAT tests it. The biggest rupee discount is the hoodie's ₹180, yet it has the smallest discount %. The cap and tote both lose exactly ₹72, which is 30% of one tag and 40% of the other. When a question says 'largest discount', check: rupees or percent?
Which discount traps does CLAT set?
- ✓Discount on CP. The banner always means off the tag.
- ✓Plain subtraction. 35% up and 20% off is 8%, not 15%.
- ✓Adding to go backwards. Bill to tag means divide by (1 − d/100).
- ✓Rupees vs percent. 'Largest discount' can point at two different items.
📌 The 'cannot be determined' trap
A tag and a discount give the selling price, never the profit. 'Tagged ₹1,200, sold at 25% off; find the profit %' needs a cost price. With no CP and no mark-up %, the answer is cannot be determined.
How has CLAT asked marked price and discount?
📝 Asked in CLAT 2018
· Q139
Mark-up then discount
The marked price of an article is 20% more than the cost price.
If the article is sold at a discount of 15% on its marked price, then the gain percent is
A5
B4½
C2½
D2
Reveal answer + reasoning
Answer: D
Take CP = ₹100. MP = ₹120. 15% of 120 = ₹18, so SP = ₹102: a gain of 2%. Shortcut: 20 − 15 − 3 = 2. Time: 20 seconds.
Why the others fail
- A — 20 − 15 treats both percentages as sitting on the same base. The discount is on ₹120, so it costs ₹18, not ₹15.
- B — No valid route gives 4½. Redo 1.2 × 0.85.
- C — A decoy: 1.2 × 0.85 = 1.02, a whole 2%.
📝 Asked in CLAT 2023
· Q145
Same SP, two discounts
World fruit production went up 54 percent between 2000 and 2019, to 883 million tonnes. … [The question adds its own pricing data.]
Frutopia and Fruitfix both sold oranges at the same selling price. However, Frutopia gave customers a 15% discount on the marked price whereas Fruitfix sold the oranges for a discount of 20% on the marked price. If the marked price of oranges on Frutopia is ₹75/kg, what is the marked price of oranges on Fruitfix?
A₹78
B₹82
C₹90
D₹80
Reveal answer + reasoning
Answer: D
Frutopia's SP = 75 × 0.85 = ₹63.75. Fruitfix reaches the same ₹63.75 after 20% off, so its tag = 63.75 ÷ 0.8 = ₹79.69, rounded to ₹80 (official key D). Fast route: 64 ÷ 0.8 = 80, so the answer is a hair under 80. Time: 30 seconds.
Why the others fail
- A — Roughly 75 plus the 5-point gap between discounts (78.75). Percentages on different tags don't transfer.
- B — Overshoots: 82 × 0.8 = 65.6, above ₹63.75.
- C — Treats 20% as a mark-up on ₹75. 90 × 0.8 = 72, nowhere near.
🧪 CLAT-style practice (not a past question)
CLAT-style: fixing a loss-maker
A fest merch stall bought tote bags at ₹120 each, tagged them at ₹180 and gave 40% off. Next year the organisers want a 20% profit on each tote bag while still advertising 40% off.
What should the new marked price be?
A₹216
B₹240
C₹192
D₹252
Reveal answer + reasoning
Answer: B
Target SP = 120 × 1.2 = ₹144. The buyer pays 60% of the tag, so MP = 144 ÷ 0.6 = ₹240. Check: 240 − 96 = 144. Shortcut: (20 + 40) ÷ 60 = 100% mark-up, i.e. double the cost. Time: 30 seconds.
Why the others fail
- A — Raises the old tag by 20% (180 × 1.2). The target is on cost, not the tag.
- C — Adds the percentages: 120 × 1.6.
- D — 180 × 1.4, with no link to the profit target.
Can you beat the sale? Myths and a quick quiz
💥 Myth vs fact
Discount myths
🙅 Myth
A 30% mark-up and a 30% discount cancel out.
Tap to bust it →
✅ Fact
1.3 × 0.7 = 0.91: a 9% loss, whatever the cost.
🙅 Myth
A bigger discount % always saves you more money.
Tap to bust it →
✅ Fact
Only on the same tag. 20% off ₹900 saves ₹180; 40% off ₹180 saves ₹72.
🙅 Myth
Discount % and profit % use the same base.
Tap to bust it →
✅ Fact
Discount sits on the tag, profit on the cost. In CLAT 2018, 15% off a 20% mark-up left just 2%.
🎯 Quick quiz
Five questions, two minutes
0 / 5
A phone cover is tagged ₹480. Meher pays ₹408.
Q1. What discount did she get?
72 ÷ 480 = 15%. 17.6% divides by the bill, the wrong base.A shopkeeper marks goods 25% above cost and gives 12% off.
Q2. What is his profit %?
25 − 12 − 3 = 10%. Check: 1.25 × 0.88 = 1.1.A store runs 'Buy 5, get 3 free' on notebooks.
Q3. What is the effective discount?
You take home 8 and pay for 5: 3 ÷ 8 = 37.5%. 60% divides by the 5 paid for.A trader marks an item 30% above cost, then offers 30% off.
Q4. What is the result?
Equal mark-up and discount lose m²/100 = 9%.A seller wants 26% profit after giving 10% off.
Q5. By what % above cost should he mark the item?
1.26 ÷ 0.9 = 1.4, so 40%. 38.6% multiplies by 1.1 instead of dividing by 0.9.🎯 Marked price and discount in a nutshell
- Mark-up is on CP; discount is on MP; profit is back on CP.
- SP = CP × (1 + m/100) × (1 − d/100); net % = m − d − md/100.
- Bill to tag: divide by (1 − d/100), never add.
- Equal mark-up and discount always lose m²/100 %.
- Tag and discount alone can't give profit: no CP means 'cannot be determined'.
📎 Formula card
- Discount % = (MP − SP) ÷ MP × 100
- SP = MP × (1 − d/100); MP = SP ÷ (1 − d/100)
- SP = CP × (1 + m/100) × (1 − d/100); net % = m − d − md/100
- Mark-up for p% profit after d% off = (p + d) ÷ (100 − d) × 100
- Equal mark-up and discount x% → loss of x²/100 %
- Buy x, get y free → discount = y ÷ (x + y) × 100 %
- Same SP after d₁ and d₂ → MP₁ : MP₂ = (100 − d₂) : (100 − d₁)
Frequently asked questions
Is discount calculated on the cost price or the marked price?
Always on the marked price, the price on the tag: Discount % = (MP − SP) ÷ MP × 100. Profit and loss, by contrast, are calculated on the cost price. Most errors in this topic come from mixing the two bases, such as taking 20% off the cost instead of off the tag.
How do you find the marked price when profit % and discount % are given?
Find the selling price you need from the cost, then divide by the share the buyer pays. For a ₹800 cost, a 20% profit target and 20% off: SP = 800 × 1.2 = ₹960, and MP = 960 ÷ 0.8 = ₹1,200. As a shortcut, the mark-up % is (p + d) ÷ (100 − d) × 100.
If the mark-up and discount are the same percentage, does the seller break even?
No. The seller always loses x²/100 %, where x is the common percentage. A 20% mark-up and a 20% discount give 1.2 × 0.8 = 0.96, a 4% loss. The discount is taken on the higher marked price, so it removes more rupees than the mark-up added.
How do you convert 'buy 2 get 1 free' into a discount percentage?
Divide the free items by the total you take home. In buy 2 get 1 free you take home 3 and pay for 2, so the discount is 1 ÷ 3, about 33.3%, not 50%. The general rule for buy x get y free is y ÷ (x + y) × 100.
Keep going
← Previous topic
Profit and Loss: CP, SP and Profit %
CP, SP and profit % on the right base, plus the traps CLAT sets
Next topic →
Successive Discounts and Discount Schemes: the Single Equivalent Discount
Why 40% + 15% off is only 49%, and how to rank any sale offer
📚
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
Successive Discounts and Discount Schemes
Two or three discounts stacked on one tag, and how to compare sale offers.
Profit and Loss: CP, SP and Profit %
The cost-price base every discount question ends on.
Successive Percentage Change
Mark-up then discount is just +m% then −d%: the a + b + ab/100 rule.
Reverse Percentage
Finding the tag from the bill is the same divide-don't-subtract move.
Every topic in Profit, Interest & Time-Speed-Work
- 1.Profit and Loss: CP, SP and Profit %
- 2.Marked Price and Discount: Mark-up, Sale Price and Profit (you're here)
- 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