Successive Percentage Change Formula

📑 On this page

⚡ The short answer

For two successive changes of a% and b%, the net change is a + b + ab/100 per cent, with decreases written as negatives. The second change acts on the new value, so it also changes the first change. Use it when one quantity changes twice or is a product (price × quantity), never for parts of a total.

🎬 The 30-second story

The viral reel that wasn't

“2,000 to 3,000 followers in one week! Up 50%!”

📈

Aarav

Aarav's dance reel takes off.

“Hot take time: pulao beats biryani.”

📱

Aarav

Next week he posts an opinion nobody asked for.

“Lost 50% of them. Fine, so I'm back to 2,000.”

📉

Aarav

Half his followers hit unfollow.

“Half of 3,000 is 1,500, genius. You're down 25%.”

🧮

Zoya

Zoya opens his profile and does the maths.

Tara's maths: The second 50% came off 3,000, not 2,000. Net = 50 − 50 + (50 × −50)/100 = −25%. A rise and an equal fall never cancel.

What is a successive percentage change?

It is one percentage change followed by another, where the second is measured on the result of the first. Think in multipliers: a 50% rise is ×1.5, a 50% fall is ×0.5, and two changes in a row are two multiplications. 1.5 × 0.5 = 0.75, a 25% fall. You never add percentages; you multiply factors.

🕒 Timeline

Aarav's followers, one multiplier at a time

👤
Start

2,000 followers

The original base. Every net answer is compared with this.
×1.5
Week 1

+50% → 3,000

50% of 2,000 = 1,000 gained.
×0.5
Week 2

−50% → 1,500

50% of 3,000 = 1,500 lost. Bigger base, bigger fall.
×0.75
Net

−25% overall

1,500 is 75% of 2,000.

How do you calculate successive percentage change?

Multiply the factors and expand: (1 + a/100)(1 + b/100) = 1 + a/100 + b/100 + ab/10,000. Strip the 1, multiply by 100, and the net change is a + b + ab/100. The first two terms you expected. The third is the one everybody forgets.

🧮 The formula

Where each piece of the formula comes from

1️⃣

first change, on the original

2️⃣

second change, on the original

🔁

ab/100

second change acting on the first change

🎯

Net % change

decreases go in as negatives

Picture a 100 × 100 square (area 10,000). Stretch the length 20% and the breadth 10%. You gain a 20 × 100 strip (20%), a 10 × 100 strip (10%) and a 20 × 10 corner of 200 units, which is 2%. That corner is ab/100: growth on growth. 120 × 110 = 13,200, a 32% rise.

📐 The figure

The ab/100 term is the corner piece

A screen that grows

Area change = 20 + 10 + (20 × 10)/100 = +32%

The 2% corner is where the first change gets changed again.

Figures are not to scale.

🎛️ Try it yourself — change any number

Try it: Aarav's two weeks

Week 1 follower change (%) Week 2 follower change (%)

Net change

−25%

₹100 becomes

₹75

a + b + ab/100 = 50 + (-50) + (50 × -50)/100 = −25%

It opens on Aarav's weeks: net −25% (the tool shows ₹100 → ₹75). Swap the order and nothing changes. Try +10 and +10: 21%, not 20%.

Why doesn't a rise and an equal fall cancel out?

Put b = −a in the formula: a − a − a²/100 = −a²/100. Always a loss, and it grows with the square of the swing. That is why a share that crashes 50% needs a 100% rise just to get back.

📊 The data

₹100 after an equal rise and then fall

+10% then −10% · loss of 1%

₹99

+20% then −20% · loss of 4%

₹96

+30% then −30% · loss of 9%

₹91

+50% then −50% · loss of 25%

₹75

Loss = x²/100. Double the swing and the loss quadruples.

📌 Order never matters

1.5 × 0.5 = 0.5 × 1.5, so +50% then −50% and −50% then +50% both end at −25%. If an option says "it depends on which change came first", it is wrong for any product-type question.

Successive percentage change: worked examples

✍️ Worked example Warm-up ⏱ 30 sec

Two raises in a row

Meher's ₹1,500 pocket money is raised 20% after her boards and another 10% on her birthday. Total increase and new amount?

1
Net = 20 + 10 + (20 × 10)/100 = 30 + 2 = 32%.
2
New amount = 1,500 × 1.32 = ₹1,980. Check: 1,500 → 1,800 → 1,980.

Answer: +32%, ₹1,980 (not the ₹1,950 a lazy 30% gives).

⚡ The exam-hall shortcut

Two rises always give a bit more than their sum. The extra is ab/100 = 2.

✍️ Worked example CLAT level ⏱ 45 sec

The fest budget rollercoaster

Rohan's fest budget of ₹80,000 is cut 25% when a sponsor pulls out. Alumni then raise the reduced budget by 40%. Final budget and net change?

1
Net = −25 + 40 + (−25 × 40)/100 = 15 − 10 = +5%.
2
Final = 80,000 × 1.05 = ₹84,000. Check: 80,000 → 60,000 → 84,000.

Answer: ₹84,000, a net rise of 5% (not 15%).

⚡ The exam-hall shortcut

Fractions: ×3/4 then ×7/5. 80,000 × 3/4 = 60,000; × 7/5 = 84,000. No decimals.

✍️ Worked example Tricky ⏱ 40 sec

Keep the bill the same

Zoya's data pack price rises 60%. By what percentage must she cut her data use to keep her bill the same?

1
Bill = price × usage. Price factor 1.6; the total factor must stay 1.
2
Usage factor = 1 ÷ 1.6 = 0.625, a cut of 37.5%. Rule: r/(100 + r) × 100 = 60/160 × 100.
3
Check: 60 − 37.5 + (60 × −37.5)/100 = 22.5 − 22.5 = 0. ✔

Answer: Cut usage by 37.5% (3/8), not 60%.

⚡ The exam-hall shortcut

+60% is ×8/5. Undo it with ×5/8, a fall of 3/8. Undoing a rise always needs a smaller fall.

✍️ Worked example Tricky ⏱ 60 sec

Three changes in a row

Kabir's café sold 12,000 cold coffees in 2023. Sales rose 10% in 2024, 20% in 2025, then fell 25% in 2026. Overall change?

1
First two: 10 + 20 + 2 = +32%.
2
Then +32 with −25: 32 − 25 + (32 × −25)/100 = 7 − 8 = −1%.
3
2026 sales = 12,000 × 0.99 = 11,880 (12,000 → 13,200 → 15,840 → 11,880).

Answer: A net fall of 1%, though the changes "add" to +5%.

⚡ The exam-hall shortcut

1.1 × 1.2 × 0.75 = 0.99. For three or more changes, fold two at a time.

What is the fastest way to solve successive percentages?

Decimals slow you down. Turn each change into a fraction multiplier and let numbers cancel. The last column gives the change that exactly undoes each one: that is how "keep the bill the same" questions die in one line.

Change	Multiplier	As a fraction	Undone by
+10%	× 1.1	11/10	−9.09% (1/11)
+20%	× 1.2	6/5	−16⅔% (1/6)
+25%	× 1.25	5/4	−20% (1/5)
+50%	× 1.5	3/2	−33⅓% (1/3)
−10%	× 0.9	9/10	+11⅑% (1/9)
−20%	× 0.8	4/5	+25% (1/4)
−25%	× 0.75	3/4	+33⅓% (1/3)
−33⅓%	× 0.667	2/3	+50% (1/2)

→ scroll to see more

💡 Estimate first: small changes nearly add

When both changes are small, ab/100 is tiny: 4% then 3% is 7.12%, so "about 7%" does if the options are 5%, 7% and 10%. With big changes (30%, 50%) the corner is large, so compute it. Check the gap between options first.

How does successive change hide in a CLAT caselet?

CLAT rarely says "successive". It hides the rule in a quantity that is a product, then changes both factors. Spot the product and the formula is instant.

🧩 At a glance

Products in disguise

🚰Expenditure

rate × consumption. Tax up, use down.

🛒Revenue

price × units sold. Price cut, sales up.

📐Area

length × breadth. Both sides change.

👥Population

this year's figure × growth factor, year after year.

🏷️Selling price

marked price × (1 − discount), discount after discount.

Mini caselet: a Ward 7 household paid ₹500 a month for water in 2023. In 2024 the tariff rose 20% and use fell 10%. In 2025 the tariff rose 25% and use fell 20%.

📊 The data

Ward 7 monthly water bill

2023 · the base

₹500

2024 · 20 − 10 − 2 = +8%

₹540

2025 · 25 − 20 − 5 = 0%

₹540

Overall 2023 → 2025: combine +8% and 0% = +8%. The tariff rose 50% in two years, yet the bill rose just 8%.

Questions write themselves. Bill change 2023 → 2025? +8%. Change in water use over two years? −10 − 20 + 2 = −28%, not −30%.

When does a + b + ab/100 fail?

🧭 Decision flow

Can I use the successive formula here?

❓ Is the same quantity changed twice, or is it a product of the changing pieces (price × quantity, l × b)?

Yes →

Use a + b + ab/100, or multiply the factors.

No ↓

❓ Is it a sum of parts, like salary = expenses + savings?

No →

Re-read and find what each % is "of". The base has shifted somewhere.

Yes ↓

❓ Does the passage give each part's share of the total?

Yes →

Take a weighted average of the changes, weighted by each part's share.

No →

Cannot be determined: pick that option if it is offered.

⚠️ Parts add, products multiply

If rent rises 10% and food 20%, total spending does not rise 32%. Rent and food are added, so the total rises by a weighted average of 10% and 20%. CLAT 2018 built a question on exactly this: the formula gives 95%, the answer is 32%.

How CLAT asked it

📝 Asked in CLAT 2019 · Q41 Rate × consumption

The Municipality of a town increases water tax by 20% and water consumption decreased by 20%. Then the percentage of increase or decrease in the monthly expenditure is:

A4% increase

B4% decrease

C5% increase

D5% decrease

Reveal answer + reasoning

Answer: B

Our solution (2019 has no official key). Expenditure = tax × consumption, a product. Net = 20 − 20 + (20 × −20)/100 = −4%; check 1.2 × 0.8 = 0.96. Time: 15 seconds.

Why the others fail

A — Right size, wrong sign. An equal rise and fall never ends above the start.
C — No valid route gives 5%.
D — A guess near 4%; the loss is exactly 20²/100.

📝 Asked in CLAT 2018 · Q137 Parts, not products

Suman saves 10% of her monthly salary. Now her expenditure increases by 30% and savings increases by 50%. The present increase in her salary is

A25%

B30%

C32%

D40%

Reveal answer + reasoning

Answer: C

Salary = expenditure + savings, a sum, so the successive formula (30 + 50 + 15 = 95%) is the trap. Take salary 100: expenditure 90 → 117, savings 10 → 15. New salary 132, a 32% rise. Weighted view: 0.9 × 30 + 0.1 × 50 = 32. Time: 40 seconds. (Options were numbered 1–4; the key gives 3.)

Why the others fail

A — Below 30%, impossible when every part rose at least 30%.
B — Ignores the 50% rise in savings.
D — The simple average of 30 and 50; expenditure carries 90% of the weight.

📝 Asked in CLAT 2025 · Q119 Change inside a budget

Mr. Das is working in a construction company. … His total monthly income includes a salary of Rs. 9228/- and a 10% house rent allowance. … Out of his total monthly income, he spends 25% on food expenses, 18% on paying the house-rent, 9% on entertainment, 23% on the education of his child, 13% on medical expenses, and he saves 12% of his total monthly income.

If the expenditure on food and entertainment is increased by 10% due to inflation in prices, what will be the new percentage of savings in the same monthly salary?

A8.4%

B8.6%

C8.8%

D8.2%

Reveal answer + reasoning

Answer: B

Work in shares; the rupees are a distraction. Food + entertainment = 25 + 9 = 34% of income. Up 10%: 34 × 1.1 = 37.4%, an extra 3.4 points. Income is unchanged, so savings fall to 12 − 3.4 = 8.6%. The change hits a part, so scale only the 34%. Time: 30 seconds.

Why the others fail

A — Takes 3.6 points off; the options sit 0.2 apart, so only exact 3.4 works.
C — Takes 3.2 points off.
D — Takes 3.8 points off.

💥 Myth vs fact

Myth or fact?

🙅 Myth

A 30% rise then a 30% fall brings you back to the start.

Tap to bust it →

✅ Fact

You end 9% below: the fall works on a bigger number.

🙅 Myth

Falling first and rising later is kinder.

Tap to bust it →

✅ Fact

Order makes no difference: 0.7 × 1.3 = 1.3 × 0.7 = 0.91.

🙅 Myth

Two 10% increases make 20%.

Tap to bust it →

✅ Fact

They make 21%; three make 33.1%. Growth on growth, like compound interest.

🙅 Myth

Any two changes in a caselet combine with a + b + ab/100.

Tap to bust it →

✅ Fact

Only if the quantities multiply. Parts of a total need a weighted average (CLAT 2018 Q137).

🎯 Quick quiz

Five quick ones: successive change

0 / 5

A phone's price rises 30% at launch, then is cut 30% in a sale.

Q1. What is the net change from the original price?

A fest stage's length goes up 20% and its breadth down 10%.

Q2. What happens to its area?

Cab fares rise 50%. Rohan wants his monthly cab spend unchanged.

Q3. By what percentage must he cut the number of rides?

Meher's study channel grows 10% a month for three months.

Q4. What is the total growth over the three months?

Zoya spends 70% of her budget on hostel rent and 30% on food. Rent rises 10%, food 20%.

Q5. By what percentage does her total spending rise?

🎯 Successive change in a nutshell

Each change acts on the new value: percentages multiply, never add.
Two changes: a + b + ab/100, falls negative.
Equal rise and fall end x²/100 below the start, in either order.
Three or more changes: fold two at a time, or multiply factors.
Products use the formula; parts of a total use a weighted average.

📎 Formula card

Net change: a + b + ab/100 %.
Multipliers: final = initial × (1 + a/100)(1 + b/100)(1 + c/100) …
Equal rise and fall: −x²/100 %.
Same rate r, n times: initial × (1 + r/100)ⁿ (growth, CI).
Keep a product constant: rise r% → cut r/(100 + r) × 100 %; fall r% → raise r/(100 − r) × 100 %.
Pairs: +25% ↔ −20%, +50% ↔ −33⅓%, +20% ↔ −16⅔%, +60% ↔ −37.5%.
Parts of a total: Σ (share × change).

Frequently asked questions

What is the formula for successive percentage change?

For two successive changes of a% and b%, the net change is a + b + ab/100 per cent, with decreases written as negatives. A 20% rise then a 10% rise gives 20 + 10 + 2 = 32%. Multiplying the factors gives the same: 1.2 × 1.1 = 1.32.

Does the order of successive percentage changes matter?

No. The result is a product of factors, and multiplication ignores order. A 25% fall then a 40% rise gives 0.75 × 1.4 = 1.05, exactly what a 40% rise then a 25% fall gives. Both are a 5% net increase, and an equal rise and fall always lose x²/100.

How do I combine three successive percentage changes?

Apply the formula twice: combine the first two, then combine that result with the third. For +10%, +20% and −25%: 10 + 20 + 2 = 32, then 32 − 25 − 8 = −1%. Or multiply the factors directly: 1.1 × 1.2 × 0.75 = 0.99, a 1% fall.

Is successive percentage change the same as compound interest?

Compound interest is a special case of it: each year's interest is a successive change at the same rate on the previous year's amount. Two years at 10% gives 10 + 10 + 1 = 21%, exactly 1.1² − 1. The extra 1% is interest earned on interest.

When should I not use the a + b + ab/100 formula?

When the changes hit parts that are added together, such as expenses and savings making up a salary. There the total change is a weighted average of the separate changes. If the passage does not give each part's share, the answer may well be 'cannot be determined'.