Successive Discount Formula and Schemes

📑 On this page

⚡ The short answer

Two discounts of a% and b% one after the other equal a single discount of a + b − ab/100, because the second discount is taken on the already-reduced price. Fastest route: multiply what you keep, (1 − a/100) × (1 − b/100). The trap: 40% + 15% is 49%, not 55%. Percentage discounts can come in any order; a flat ₹ coupon cannot.

🎬 The 30-second story

The two-store kurta hunt

“Same kurta, ₹2,400. Store A: flat 50% off. Store B: 40% plus an extra 15%!”

🛍️

Meher

Festive sale week, two tabs open.

“40 + 15 = 55. Store B is cheaper. Easy.”

🧮

Meher

She adds the banner numbers.

“40% off leaves ₹1,440. The extra 15% is on ₹1,440, not ₹2,400.”

🧾

Zoya

Zoya reads the small print.

“₹1,224 at B. ₹1,200 at A. The 'bigger' offer costs me ₹24 more?”

😳

Meher

The two-step offer is really 49% off.

Tara's maths: The extra 15% only touches the ₹1,440 left, so it saves ₹216, not ₹360. Total: ₹1,176 off ₹2,400 = 49%. Store A's flat 50% wins.

What is a successive discount?

A successive discount is two or more discounts applied one after another, each on the price left by the one before: 'sale plus an extra 10% for app users', 'season sale plus a festive coupon'. Only the first discount is on the marked price. Every later one is on a smaller number.

🕒 Timeline

Store B's kurta, one step at a time

1
Marked price

₹2,400 on the tag

The base for the first discount only.
2
40% off

₹2,400 × 0.6 = ₹1,440

₹960 saved, worked out on ₹2,400.
3
Extra 15% off

₹1,440 × 0.85 = ₹1,224

₹216 saved, worked out on ₹1,440, not ₹2,400.
=
Single equivalent

₹1,176 off ₹2,400 = 49%

The one number you compare across stores.

How do you calculate successive discounts?

Track what you keep, not what you lose. After 40% off you keep 0.6 of the price. After an extra 15% you keep 0.85 of that. So you keep 0.6 × 0.85 = 0.51 of the tag, a 49% discount.

🧮 The formula

Multiply what you keep

🏷️

Marked price

the tag

✂️

(1 − a/100)

keep after discount 1

✂️

(1 − b/100)

keep after discount 2

🧾

Final price

single discount = a + b − ab/100

Expand the bracket and the shortcut falls out: the single discount is a + b − ab/100. For Store B: 40 + 15 − 6 = 49%. It is the successive change rule with both changes negative.

🟦 Picture the percent

Where did the missing 6% go?

What Meher assumed

Both discounts on the full tag

Off (40 + 15)You pay

What really happens

The 15% never touches the first 40 squares

First 40% offExtra 15% of the 60 leftYou pay

The extra 15% hits only the 60 squares still standing, so it removes 9, not 15. The 6 'lost' squares are 15% of the 40 already gone: the ab/100 term, a discount on a discount that no shop gives.

🎛️ Try it yourself — change any number

Stack the discounts yourself

Sale discount (%) Extra discount on sale price (%) Coupon discount (%, 0 if none)

Single equivalent discount

49%

₹1,000 tag becomes

₹510

1 − (0.6 × 0.85) = 49%, not 55%

It opens on Store B: 49%, not 55%. Try 20 and 20 (36%), then 10, 10 and 10 (27.1%). Swap the first two boxes: nothing moves.

Successive discount: worked examples

✍️ Worked example Warm-up ⏱ 25 sec

Earbuds with a bank-card bonus

Earbuds are tagged ₹3,000: 25% off, then 10% off the sale price for bank-card users. What does Aarav pay, and what is the single discount?

1
After 25% off: 3,000 × 0.75 = ₹2,250.
2
Extra 10%: 2,250 × 0.9 = ₹2,025.
3
975 ÷ 3,000 = 32.5% off.

Answer: ₹2,025, a single discount of 32.5%, not 35%.

⚡ The exam-hall shortcut

25 + 10 − 2.5 = 32.5%; 3,000 × 0.675 = ₹2,025.

✍️ Worked example CLAT level ⏱ 40 sec

Three discounts on a laptop

Kabir lists a laptop at ₹50,000 with successive discounts of 20%, 10% and 5%. Final price and single discount?

1
Keep-factors: 0.8 × 0.9 × 0.95 = 0.684.
2
50,000 × 0.684 = ₹34,200.
3
1 − 0.684 = 31.6% off.

Answer: ₹34,200; single discount 31.6%, not 35%.

⚡ Pair them up

Pair them: 20 and 10 → 28. Then 28 and 5 → 28 + 5 − 1.4 = 31.6%.

✍️ Worked example CLAT level ⏱ 40 sec

Back to the tag

Zoya pays ₹1,377 for a backpack after successive discounts of 15% and 10%. What was the marked price?

1
Keep-factor: 0.85 × 0.9 = 0.765.
2
Tag × 0.765 = 1,377, so tag = 1,377 ÷ 0.765 = ₹1,800.
3
Check: 1,800 → 1,530 → 1,377. ✓

Answer: Marked price = ₹1,800.

⚡ The exam-hall shortcut

Never add 23.5% to ₹1,377 (that gives ₹1,700.60). The 23.5% sat on the tag, so divide.

✍️ Worked example Tricky ⏱ 35 sec

Find the hidden second discount

A smartwatch tagged ₹800 gets 20% off, then a second discount at checkout. Rohan pays ₹544. What was the second discount?

1
After the first discount: 800 × 0.8 = ₹640.
2
The second cut: 640 − 544 = ₹96.
3
Measure it on ₹640: 96 ÷ 640 = 15%.

Answer: The second discount was 15%.

⚡ The exam-hall shortcut

544 ÷ 640 = 0.85: 15% off. Trap: 96 ÷ 800 = 12% uses the tag.

Does the order of successive discounts matter?

For percentage discounts, no: 0.6 × 0.85 = 0.85 × 0.6. A flat rupee coupon is different, because ₹200 off is a bigger share of a smaller price.

⚔️ Side by side

Percent with percent vs percent with a ₹ coupon

🔁% then %

Order never matters

•0.8 × 0.9 = 0.9 × 0.8 = 0.72
•₹1,500 tag: ₹1,080 either way
•Just multiply the keep-factors

⚠️% and flat ₹

Order changes the bill

•₹1,500 tag, 20% off and a ₹200 coupon
•20% first, then ₹200: ₹1,000
•₹200 first, then 20%: ₹1,040

Test	% then %	% and flat ₹
Why	Both cuts scale the price	The 20% also shrinks the coupon if the coupon goes first
Buyer prefers	Doesn't matter	Percent first, coupon last

Coupon first means the 20% is taken on ₹1,300, so it is worth ₹260 instead of ₹300. That ₹40 is the gap.

How do you compare discount schemes quickly?

Convert every offer into one number: the percentage of the tag you do not pay. For 'buy n, get m free' you pay for n of n + m items, so the discount is m ÷ (n + m), not m ÷ n.

Scheme	You pay for	Single discount
50% + extra 20%	0.5 × 0.8 = 0.4	60%
Flat 55%	0.45	55%
Buy 3, get 2 free	3 of 5 items	40%
Buy 2, get 1 free	2 of 3 items	33⅓%
Buy 1, get the 2nd at 50% off	1.5 of 2 items	25%
'Up to 70% off'	unknown	cannot be determined

→ scroll to see more

🧩 At a glance

Exam-hall shortcuts

✖️Keep-factors

Multiply (1 − d/100) for every discount, however many.

➕Two at a time

a + b − ab/100. Three? Pair two, then pair the result with the third.

🪞Equal discounts

d% twice = 2d − d²/100. 20% and 20% = 36%.

🍕Fractions

25% + 20%: keep 3/4 × 4/5 = 3/5, so 40% off.

💡 Bracket the answer before you calculate

The single discount is always more than the biggest discount and less than the plain sum. 30% + 25% must sit just under 55% (it is 47.5%). With options 25%, 47.5%, 55% and 57.5%, three die without multiplying.

How do successive discounts hide in a CLAT caselet?

CLAT hides this in a paragraph: A speaker is tagged ₹6,000 on four sites. P gives 35% off. Q gives 20% off and a further 20% at checkout. R gives 25% off, 10% more for app users, then a ₹200 coupon. S runs 'buy 2, get 1 free' for a group buying three. Then it asks which site is cheapest per speaker. Draw it.

📊 The data

Price per speaker on each site (tag ₹6,000)

Site P · 6,000 × 0.65

₹3,900

Site Q · 6,000 × 0.8 × 0.8 = 36% off

₹3,840

Site R · 6,000 × 0.75 × 0.9 = 4,050, then − 200

₹3,850

Site S · 12,000 for 3 speakers

₹4,000

Q wins by ₹10. R, with three offers, comes second; the 'free' speaker at S is the worst deal.

Two 20% cuts (36%) still beat a flat 35%. R's ₹200 coupon is only about 4.9% of the ₹4,050 it is applied to. S's free speaker is just 33⅓% off. And if the caselet asks for a site's profit with no cost price, the answer is 'cannot be determined'.

Which successive discount traps does CLAT set?

✓Adding the discounts. 25% + 10% is 32.5%, not 35%.
✓Second discount on the tag. 'Extra 10% on the sale price' means 10% of the reduced price.
✓Adding to go backwards. Final price to tag: divide by the keep-factor.
✓Free-item maths. Buy 2, get 1 free is 33⅓%, not 50%.

⚠️ 'Up to' and 'flat' are different promises

'Flat 40% off' is 40% on every item. 'Up to 40% off' only caps the biggest discount. Asked what a shopper saved under an 'up to' offer with no item-wise discount? Cannot be determined.

How has CLAT asked successive discounts?

📝 Asked in CLAT 2023 · Q145 Two schemes, one selling price

World fruit production went up 54 percent between 2000 and 2019, to 883 million tonnes. Five fruit species accounted for 57 percent of the total production in 2019, down from 63 percent in 2000. … [This 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

Common selling price: Frutopia keeps 85% of ₹75, so SP = 75 × 0.85 = ₹63.75. Fruitfix's tag × 0.8 = 63.75, so its tag = 63.75 ÷ 0.8 = ₹79.6875, about ₹80. Shortcut: 75 × 0.85 ÷ 0.8 = 75 × 17/16. A bigger discount needs a bigger tag to reach the same price. Time: 30 seconds. D is the nearest option and the official answer.

Why the others fail

A — ₹78 × 0.8 = ₹62.40, below ₹63.75.
B — ₹82 × 0.8 = ₹65.60, above ₹63.75.
C — ₹90 is ₹75 plus 20%: it treats the discount as a mark-up. ₹90 × 0.8 = ₹72.

🧪 CLAT-style practice (not a past question) CLAT-style: member discount on a sale

During its anniversary week, a bookstore offers 25% off the marked price of every box set. Members of its reading club get an additional 12% off the discounted price. Aarav, a member, pays ₹1,320 for a fantasy box set.

What was the marked price of the box set?

A₹1,760

B₹2,000

C₹2,095.24

D₹1,808.40

Reveal answer + reasoning

Answer: B

Aarav keeps 0.75 × 0.88 = 0.66 of the tag (25 + 12 − 3 = 34% off). Tag = 1,320 ÷ 0.66 = ₹2,000. Check: 2,000 → 1,500 → 1,320. ✓ Time: 30 seconds.

Why the others fail

A — 1,320 ÷ 0.75 forgets the member's extra 12%.
C — 1,320 ÷ 0.63 adds the discounts into a single 37%.
D — 1,320 × 1.37 adds 37% back instead of dividing.

Can you beat the sale? Myths and a quick quiz

💥 Myth vs fact

Successive discount myths

🙅 Myth

20% off plus another 20% off is 40% off.

Tap to bust it →

✅ Fact

0.8 × 0.8 = 0.64, so you pay 64%: a 36% discount.

🙅 Myth

The order of two percentage discounts changes the final price.

Tap to bust it →

✅ Fact

0.9 × 0.7 = 0.7 × 0.9. Order matters only when one of the discounts is a flat rupee amount.

🙅 Myth

Buy 2, get 1 free is half price.

Tap to bust it →

✅ Fact

You pay for 2 of 3 items: 33⅓% off, less than a flat 35%.

🙅 Myth

Three 10% discounts make 30% off.

Tap to bust it →

✅ Fact

0.9 × 0.9 × 0.9 = 0.729, so the discount is 27.1%.

🎯 Quick quiz

Five questions, two minutes

0 / 5

A jacket gets 35% off and then a further 20% off the sale price.

Q1. What is the single equivalent discount?

A store gives three successive discounts of 10% each.

Q2. What is the overall discount?

Scheme X: buy 4, get 1 free. Scheme Y: 12% off, then an extra 10%. Scheme Z: a flat 21% off.

Q3. Which scheme is best for the buyer?

Meher pays ₹2,736 for a phone after successive discounts of 20% and 5%.

Q4. What was the marked price?

A pair of shoes is tagged ₹2,500. Rohan can use a 20% sale discount and a ₹300 coupon, in either order.

Q5. What is the least he can pay?

🎯 Successive discounts in a nutshell

Each later discount is taken on the reduced price, never the tag.
Single discount = a + b − ab/100; for three or more, multiply keep-factors.
It lies between the largest discount and the plain sum.
Final price to tag: divide by the keep-factors.
Buy n, get m free = m ÷ (n + m); a ₹ coupon is best applied last.

📎 Formula card

Final price = MP × (1 − a/100) × (1 − b/100) × (1 − c/100) …
Two discounts → a + b − ab/100
d% twice → 2d − d²/100 (20, 20 → 36%)
MP = final price ÷ [(1 − a/100)(1 − b/100)]
Buy n, get m free → m ÷ (n + m) × 100% off
Same SP, two discounts → MP₂ = MP₁ × (100 − d₁) ÷ (100 − d₂)

Frequently asked questions

What is the formula for successive discounts?

For two discounts of a% and b%, the single equivalent discount is a + b − ab/100, so 30% and 20% give 30 + 20 − 6 = 44%. For three or more, multiply the fractions you keep: 20%, 10% and 5% give 0.8 × 0.9 × 0.95 = 0.684, a 31.6% discount.

Is a 20% discount followed by 10% the same as 30% off?

No. The second 10% is taken on the reduced price, not the tag. On ₹100, 20% off leaves ₹80, and 10% of ₹80 is ₹8, so you pay ₹72: a 28% discount. The missing two points are the ab/100 term.

Does the order of successive discounts matter?

Not for percentage discounts, because 0.8 × 0.9 equals 0.9 × 0.8. It does matter with a flat rupee coupon. On a ₹1,500 tag with 20% off and a ₹200 coupon, percent first gives ₹1,000 and coupon first gives ₹1,040, so apply the coupon last.

Is buy 2 get 1 free better than 30% off?

Slightly. You pay for 2 of every 3 items, a discount of 1 ÷ 3, or 33⅓%, which beats 30% but loses to a flat 35%. It only helps if you actually want three items, which is why CLAT often asks for the cost per item.

How do you find the marked price from the final price after successive discounts?

Divide the final price by the product of the fractions kept. Paid ₹1,377 after 15% and 10% off? The fraction kept is 0.85 × 0.9 = 0.765, so the tag was 1,377 ÷ 0.765 = ₹1,800. Never add the percentages back to the bill.