Percentage Increase & Decrease: % More Than

Q: How do you calculate percentage increase?

Subtract the old value from the new one, divide by the old value and multiply by 100. A thali going from ₹80 to ₹92 rises by 12 ÷ 80 × 100 = 15%. The old value is the base because change is measured from where you started.

Q: What is the difference between '% more than' and '% less than'?

Same gap, different base: the number after 'than'. With 1,500 followers against Aarav's 1,000, Zoya has 500 ÷ 1,000 = 50% more, while Aarav has 500 ÷ 1,500 = 33⅓% less. The 'less than' figure is always smaller because it divides by the bigger number.

Q: If A is 20% more than B, by what percent is B less than A?

16⅔%. Put B = 100, so A = 120. The gap is 20 and the base is now A, so 20 ÷ 120 = 1/6 = 16⅔%. In general, if A is x% more than B, then B is x ÷ (100 + x) × 100 per cent less than A.

Q: Can a percentage increase be more than 100%?

Yes. ₹200 to ₹700 is a 250% increase, because the ₹500 gap is two and a half times the base. A decrease cannot exceed 100%, since a 100% fall already reaches zero. Note that 200% more means three times, not double.

📑 On this page

⚡ The short answer

Percentage change = (new − old) ÷ old × 100. For 'A is what % more or less than B', the base is whatever comes after than. The trap: if A is 50% more than B, B is only 33⅓% less than A. Same gap, bigger base.

🎬 The 30-second story

The follower fight

“1,500 followers! Aarav, you're stuck at 1,000.”

📱

Zoya

Zoya's reel blew up.

“You have 50% more than me, so I have 50% less. Same thing.”

🧮

Aarav

Aarav flips the sentence, keeps the number.

“50% less than 1,500 is 750. Do you have 750?”

➗

Zoya

Zoya tests the claim.

“…I have 1,000. So what am I?”

😳

Aarav

The gap is 500 either way. Only the base moved.

Tara's maths: Zoya is 500 ÷ 1,000 = 50% more than Aarav. Aarav is 500 ÷ 1,500 = 33⅓% less than Zoya. The number after than goes at the bottom.

What is percentage change, really?

Percentage change answers one question: how big is the change compared with where you started? A ₹600 rise is huge on ₹2,000 of pocket money and pocket lint on a ₹2 lakh salary. So we measure change per hundred of the start.

🟦 Picture the percent

₹2,000 pocket money becomes ₹2,600

Old = 100%

each square = ₹20

Rise = 30%

₹600 ÷ ₹20 = 30 squares

🧮 The formula

The only formula you need

📈

Change

new − old

🧱

Base

the starting value

💯

× 100 = % change

Read it as a fraction: 600/2,000 = 3/10 = 30%. The × 100 just converts to 'per hundred'. A decrease can never pass 100% (you can't lose more than everything); an increase can be 300%.

Which number goes at the bottom?

Nearly every percentage-change mistake is the same one: the wrong denominator. The gap on top is easy. The sentence always names the base, if you read it slowly.

🧭 Decision flow

Find the base in ten seconds

❓ Does the question say 'more than' or 'less than'?

Yes →

Base = the quantity after 'than'

'Girls are what % more than boys?' → boys

No ↓

❓ Is it a change over time, 'from 2011 to 2012'?

Yes →

Base = the earlier value

No ↓

❓ Does it say 'as a percentage of …'?

Yes →

Base = whatever follows 'of'

No →

A share question: base = the total

📌 The 'than' rule

A is what % more than B? → (A − B) ÷ B × 100.
B is what % less than A? → (A − B) ÷ A × 100.
The gap never changes. Whatever sits after 'than' moves to the bottom.

Is 'A is x% more than B' the same as 'B is x% less than A'?

No. This one idea sits behind more CLAT Quant questions than anything else here. The follower fight, to scale:

📊 The data

Same 500-follower gap, two different bases

Zoya · base for 'less than Zoya'

1,500

Aarav · base for 'more than Aarav'

1,000

500 ÷ 1,000 = 50% more. 500 ÷ 1,500 = 33⅓% less.

⚔️ Side by side

One gap, two questions

⬆️More than

Zoya compared with Aarav

•Zoya has 50% more than Aarav

⬇️Less than

Aarav compared with Zoya

•Aarav has 33⅓% less than Zoya

Test	More than	Less than
Gap	500	500
Base (after 'than')	Aarav: 1,000	Zoya: 1,500
Answer	500/1,000 = 50%	500/1,500 = 33⅓%

'Less than' divides by the bigger number, so it is always smaller.

The bridge: if A is x% more than B, B is x ÷ (100 + x) × 100% less than A. If A is x% less than B, B is x ÷ (100 − x) × 100% more than A. Don't cram these; put B = 100 and they fall out.

If A is … than B	then B is … than A	why
10% more	9.09% less	10/110
20% more	16⅔% less	20/120 = 1/6
50% more	33⅓% less	50/150 = 1/3
100% more (double)	50% less (half)	100/200
20% less	25% more	20/80 = 1/4
25% less	33⅓% more	25/75 = 1/3
50% less (half)	100% more (double)	50/50

→ scroll to see more

🎛️ Try it yourself — change any number

Flip the base yourself

Aarav's followers Zoya's followers

Change

+500

New vs old (base = old)

+50%

Old vs new (base = new)

−33.33%

(1,500 − 1,000) ÷ 1,000 × 100 = +50%

Line two is 'Zoya is what % more?'; line three is 'Aarav is what % less?'. Try 80 and 100, then 50 and 100.

How do you calculate percentage increase and decrease? Three worked examples

✍️ Worked example Warm-up ⏱ 20 sec

The thali price hike

The hostel canteen thali went from ₹80 to ₹92. By what percentage did the price rise?

1
Change = 92 − 80 = ₹12.
2
It's a change over time, so the base is the old price, ₹80.
3
12 ÷ 80 = 3/20 = 15%.

Answer: A 15% rise.

⚡ The exam-hall shortcut

Ratio route: 92 ÷ 80 = 1.15, so +15%.

✍️ Worked example CLAT level ⏱ 40 sec

The phone that has to climb back

Rohan's phone dropped from ₹24,000 to ₹18,000 in a sale. (a) What was the % decrease? (b) What % rise takes it back to ₹24,000?

1
(a) ₹6,000 on a base of ₹24,000: 1/4 = 25% decrease.
2
(b) Same ₹6,000, but the climb starts from ₹18,000: 1/3 = 33⅓% increase.

Answer: (a) 25% decrease; (b) 33⅓% increase.

⚡ Remember

Undoing an x% fall always needs more than an x% rise: the climb starts from a smaller base.

✍️ Worked example Tricky ⏱ 50 sec

Three friends, no marks given

In a mock, Meher scores 25% less than Rohan, and Aarav scores 20% more than Rohan. Meher's score is what percentage less than Aarav's?

1
No marks given, so let Rohan = 100.
2
Meher = 75. Aarav = 120.
3
'Less than Aarav', so base 120: 45/120 = 37.5%.

Answer: 37.5% less. Flip it and Aarav is 45/75 = 60% more than Meher.

⚡ Trap to avoid

Don't add 25 and 20 to get 45%. Those sit on Rohan's base; the answer sits on Aarav's.

What is the fastest way to find percentage change in the exam?

1
Simplify to a fraction
28 ÷ 140 looks ugly until you see 1/5 = 20%.
2
Or divide new by old
168 ÷ 140 = 1.2, so +20%; 0.85 means −15%.
3
Estimate, then read the options
5,000 ÷ 15,300 is a little under 33⅓%. With banded options, you're done.
4
Check the direction
'More than' always beats the matching 'less than'. If not, wrong base.

💡 The 1/n ↔ 1/(n + 1) shortcut

Strike rates: Meher 168, Rohan 140. Meher is 28/140 = 1/5 = 20% more; Rohan is 28/168 = 1/6 = 16⅔% less. Whenever 'more' is 1/n, 'less' is 1/(n + 1): 1/2 ↔ 1/3 (50% ↔ 33⅓%), 1/4 ↔ 1/5 (25% ↔ 20%).

How does CLAT hide percentage change inside a caselet?

CLAT never just hands you two numbers. It gives a paragraph of shares and you build the numbers. CLAT 2024's workers passage: 3,00,000 workers, 48% rural; self-employed are 56% of rural and 40% of urban; regular salaried 12% and 48%; casual wage 32% and 12%.

Category	Rural (1,44,000)	Urban (1,56,000)
Self-employed	56% → 80,640	40% → 62,400
Regular salaried	12% → 17,280	48% → 74,880
Casual wage	32% → 46,080	12% → 18,720

→ scroll to see more

📊 The data

Workers by type (CLAT 2024, passage XX)

RuralUrban

Self-employed

80,640

62,400

Regular salaried

17,280

74,880

Casual wage

46,080

18,720

Build the table once; every question is then one division.

✍️ Worked example CLAT level ⏱ 60 sec

CLAT 2024 Q115: rural vs urban self-employed

By what percentage the number of self-employed workers in rural areas is more than the number of self-employed workers in urban areas? (A) 29.23 (B) 33.24 (C) 35.01 (D) 34.32

1
Rural = 1,44,000; urban = 1,56,000.
2
Self-employed: rural 80,640; urban 62,400.
3
'More than urban': 18,240 ÷ 62,400 = 29.23%.

Answer: (A) 29.23%, the official key.

⚡ 30-second route

Skip the 3,00,000. Rural ∝ 48 × 56 = 2,688; urban ∝ 52 × 40 = 2,080. 2,688 ÷ 2,080 = 1.2923, so +29.23%.

'More than' has no ceiling: urban salaried workers (74,880) are 333⅓% more than rural (17,280), i.e. 4⅓ times. Flip it and rural is only 76.9% less.

Which traps cost the most marks?

🧩 At a glance

Three ways CLAT catches you

🔁The flipped base

Dividing by the bigger number in a 'more than' question. In CLAT 2023 Q137 that slip is option A.

↕️More or less?

CLAT 2020 Q136 put '29.7% more' beside '28.6% less'. Check which is bigger first.

📊% change of a %

A profit rate going from 50% to 60% is a 10-point rise but a 20% increase.

⚠️ When the numbers are already percentages

CLAT 2021 gave only profit rates: Contigent 50% (2011) → 60% (2012); Pollaris 20% (2010) → 35% (2011). Q136's key is 20% (10 ÷ 50), not 10%; Q140's is 75% (15 ÷ 20). 'Cannot be determined' tempts, since rupee profits are never given, but the key took change ÷ old rate.

How has CLAT asked percentage change?

Paper	What it compared	Base	Answer
2020 Q136	WB females vs Odisha females	Odisha (21k)	28.6% less
2021 Q136	Contigent profit rate, 2011 → 2012	50% (2011)	20%
2021 Q140	Pollaris profit rate, 2010 → 2011	20% (2010)	75%
2022 Q137	Fine Arts girls vs boys	boys (230)	47.82%
2023 Q137	non-SC/ST vs SC/ST pay	SC/ST (₹15,300)	30–35%
2024 Q110	State 2 petrol vs State 1 diesel	diesel (450)	6.67%
2024 Q115	rural vs urban self-employed	urban (62,400)	29.23%

→ scroll to see more

Seven questions, one skill: put the word after 'than' (or the 'from' year) at the bottom. Three in full:

📝 Asked in CLAT 2023 · Q137 Wrong base is an option

…The mean income for Scheduled Castes or Scheduled Tribes ("SC/ST") persons in urban areas who are in regular employment is ₹15,300 as against ₹20,300 for persons belonging to the non-SC/ST category… [Note: Values have been approximated to the nearest hundred]

Of the regular employed in urban areas, the earnings of a non-SC/ST worker is what percent more than a SC/ST worker?

ABetween 20% and 25%

BLess than 15%

CBetween 30% and 35%

DMore than 35%

Reveal answer + reasoning

Answer: C

'More than a SC/ST worker', so the base is ₹15,300. Gap = ₹5,000. 5,000 ÷ 15,300 = 32.68%, between 30% and 35%. Estimate: 5,000/15,000 = 33⅓%, nudged lower by the bigger base. Time: 30 seconds.

Why the others fail

A — 5,000 ÷ 20,300 = 24.6%: the flipped base. That is how much less the SC/ST worker earns.
B — Under 15% would need a gap below ₹2,295.
D — Over 35% would need a gap above ₹5,355.

📝 Asked in CLAT 2020 · Q136 'Less than': direction and base

The following data presents the cases of Japanese Encephalitis in five states of India. Number of persons affected (in thousands), from the bar chart: Odisha 57, West Bengal 45, Chhattisgarh 21, Jharkhand 29, Andhra Pradesh 13. Ratio of males to females: Odisha 12 : 7, West Bengal 6 : 3, Chhattisgarh 5 : 2, Jharkhand 15 : 14, Andhra Pradesh 7 : 6.

Number of females affected by Japanese encephalitis in West Bengal are what percentage (up to 1 decimal) more or less than that of females affected in Odisha?

A28.6 % less

B29.7 % more

C26.8 % less

D25.8 % more

Reveal answer + reasoning

Answer: A

Odisha females = 57 × 7/19 = 21 thousand; West Bengal = 45 × 3/9 = 15 thousand. West Bengal is smaller, so less, and the base is the state after 'than', Odisha: 6 ÷ 21 = 2/7 ≈ 28.6% less. Time: 45 seconds.

Why the others fail

B — Wrong direction: West Bengal has fewer affected females, so 'more' is impossible.
C — Digits swapped (26.8 for 28.6): a careless-reading decoy.
D — Wrong direction again.

📝 Asked in CLAT 2022 · Q137 Base named in the question

As per a survey conducted in a college, out of total students enrolled, i.e., 3,000 in 2020-21, 1,700 were girls and 1,300 were boys. … 19% of the total students opted Fine Arts and the percentage of girls who opted Fine Arts was 20% of the total number of girls.

Girls have outnumbered boys in Fine Arts. How many girls in Fine Arts are more than the boys, as a percentage of total number of boys in Fine Arts?

A49.62%

B47.82%

C51.23%

D50.89%

Reveal answer + reasoning

Answer: B

Fine Arts = 19% of 3,000 = 570. Girls = 20% of 1,700 = 340, so boys = 230. The base is named: 'as a percentage of … boys'. 110 ÷ 230 = 47.826%, printed as 47.82% (cut off, not rounded). Time: 60 seconds.

Why the others fail

A — Near-miss decoy: 110 ÷ 230 is just under 48%.
C — Over 50% needs girls above 1.5 × 230 = 345; there are 340.
D — Same check: 340 < 345 rules out 50%+.

Myths, a quiz and your formula card

💥 Myth vs fact

Unlearn these

🙅 Myth

If A is 40% more than B, then B is 40% less than A.

Tap to bust it →

✅ Fact

B is 40/140 = 28.6% less. The gap is the same; the base isn't.

🙅 Myth

A percentage change can't be more than 100%.

Tap to bust it →

✅ Fact

An increase can: ₹200 to ₹700 is +250%. Only a decrease stops at 100%.

🙅 Myth

'200% more' means double.

Tap to bust it →

✅ Fact

Double is 100% more. 200% more is three times the original.

🎯 Quick quiz

Five quick ones: find the base

0 / 5

Fest sponsorship went from ₹1,60,000 to ₹2,00,000.

Q1. What is the percentage increase?

Rohan uses 30 GB of data a month; Zoya 24 GB.

Q2. Zoya's use is what percent less than Rohan's?

A café's daily orders are 60% more than last month's.

Q3. Last month's orders were what percent less than today's?

Village P has 4,500 voters; village Q has 1,500.

Q4. P has what percent more voters than Q?

A coaching batch's pass rate rose from 40% to 50%.

Q5. By what percent did the pass rate increase?

🎯 Percentage change in a nutshell

% change = (new − old) ÷ old × 100.
'More/less than': base = whatever follows than.
x% more ↔ x ÷ (100 + x) × 100 % less. 50% more = 33⅓% less.
x% less ↔ x ÷ (100 − x) × 100 % more. 20% less = 25% more.
No numbers? Set the reference to 100.

📎 Formula card

% change = (new − old) ÷ old × 100
A is what % more than B = (A − B) ÷ B × 100
B is what % less than A = (A − B) ÷ A × 100
Flip: x% more → x/(100 + x) × 100 % less; x% less → x/(100 − x) × 100 % more
Fraction pairs: 1/n more ↔ 1/(n + 1) less
Ratio route: new ÷ old = 1.18 → +18%; 0.85 → −15%
Times vs more: k times as much = (k − 1) × 100 % more

Frequently asked questions

How do you calculate percentage increase?

Subtract the old value from the new one, divide by the old value and multiply by 100. A thali going from ₹80 to ₹92 rises by 12 ÷ 80 × 100 = 15%. The old value is the base because change is measured from where you started.

What is the difference between '% more than' and '% less than'?

Same gap, different base: the number after 'than'. With 1,500 followers against Aarav's 1,000, Zoya has 500 ÷ 1,000 = 50% more, while Aarav has 500 ÷ 1,500 = 33⅓% less. The 'less than' figure is always smaller because it divides by the bigger number.

If A is 20% more than B, by what percent is B less than A?

16⅔%. Put B = 100, so A = 120. The gap is 20 and the base is now A, so 20 ÷ 120 = 1/6 = 16⅔%. In general, if A is x% more than B, then B is x ÷ (100 + x) × 100 per cent less than A.

Can a percentage increase be more than 100%?

Yes. ₹200 to ₹700 is a 250% increase, because the ₹500 gap is two and a half times the base. A decrease cannot exceed 100%, since a 100% fall already reaches zero. Note that 200% more means three times, not double.