Ratio and Proportion Basics for CLAT: Simplify & Compare

📑 On this page

⚡ The short answer

A ratio a : b means 'for every a of the first, b of the second'. It is the fraction a/b, so you may multiply or divide both terms by the same number, never add. To compare a : b with c : d, compare a × d with b × c. The trap: a ratio alone never gives the actual numbers.

🎬 The 30-second story

Who is the better captain?

“My team won 12. Rohan's won 9. Case closed.”

🏏

Aarav

Aarav has played 20 matches; Rohan, 15.

“Win : loss is 12 : 8 for you, 9 : 6 for him. Both are 3 : 2. Level.”

📒

Zoya

Zoya divides by 4 and by 3.

“Fine. We both win the next 5. Still level?”

🏆

Aarav

Five more wins each.

“17 : 8 vs 14 : 6. 17 × 6 = 102, 8 × 14 = 112. He's ahead.”

🧮

Zoya

Same 5 wins, different result.

Tara's maths: Both started at 3 : 2. A ratio survives only multiplying or dividing. Add the same 5 wins and the smaller record moves more, because 5 is a bigger chunk of 9 than of 12.

What is a ratio, really?

A ratio compares two quantities of the same kind by division. Boys to girls 3 : 2 does not mean 3 boys. It means the class splits into equal parts: 3 parts boys, 2 parts girls. The class could have 15 students or 1,500.

🧮 The formula

Every ratio hides a parts count

👦

3 parts boys

👧

2 parts girls

🏫

5 parts = the class

🟦 Picture the percent

Boys : girls = 3 : 2 on 100 squares

3 : 2

One part = 20 squares.

Boys: 3/5 = 60%Girls: 2/5 = 40%

So one ratio gives three facts. Boys are 3/5 = 60% of the class, girls 2/5 = 40%, and boys are 3/2 = 1.5 times the girls. The 5 comes from adding the terms.

⚔️ Side by side

Part-to-part or part-to-whole?

⚖️Part : part

boys : girls = 3 : 2

•Compares two slices
•Boys are 3/2 = 1.5 × girls

🥧Part : whole

boys : class = 3 : 5

•Compares a slice with everything
•Boys are 3/5 = 60% of the class

Test	Part : part	Part : whole
Classic slip	Girls are 2/3 of the class	Boys : girls = 3 : 5

Ask first: is the second term another part, or the total?

How do you simplify a ratio?

Like a fraction: divide both terms by their highest common factor (HCF). Clean the terms first: same units, no decimals, no fractions.

Messy ratio	Clean it by	Simplest
18 : 24	÷ HCF 6	3 : 4
2 m : 75 cm	200 : 75, then ÷ 25	8 : 3
0.4 : 1.25	× 100 → 40 : 125, ÷ 5	8 : 25
25% : 15% of one total	drop the %, ÷ 5	5 : 3

→ scroll to see more

✍️ Worked example Warm-up ⏱ 30 sec

Cold coffee in three fractions

Zoya's cold coffee uses 1/2 cup coffee, 2/3 cup milk and 3/4 cup ice. Write coffee : milk : ice in whole numbers.

1
Clear the fractions by multiplying every term by the same number: the LCM of 2, 3 and 4, which is 12.
2
1/2 × 12 = 6, 2/3 × 12 = 8, 3/4 × 12 = 9.
3
6, 8 and 9 share no common factor, so stop.

Answer: 6 : 8 : 9

⚡ The exam-hall shortcut

Multiplying by 12 is just making a 12-times batch: 6, 8 and 9 cups. Same taste, same ratio.

💡 Scale, don't panic

Multiply every term by the same number and the ratio holds. Decimals: × 10 or 100 until they vanish. Fractions: × the LCM of the denominators. Then divide by the HCF.

How do you compare two ratios quickly?

CLAT rarely says 'simplify'. It asks which is larger, or whether a ratio rose. Pick the tool the numbers suit.

1
Cross-multiply
a : b vs c : d → compare a × d with b × c. 3 : 4 vs 5 : 7 → 21 vs 20, so 3 : 4 wins.
2
Common term
3 : 4 = 21 : 28 and 5 : 7 = 20 : 28. Same second term, so the bigger first term wins.
3
Benchmark
Test each against a round number like 1/2 or 1. One above, one below? Done.

✍️ Worked example CLAT level ⏱ 50 sec

Followers per following

Account A: 4,800 followers, 360 following. B: 2,100 and 150. C: 6,300 and 500. Which has the highest followers : following ratio?

1
Simplify. A = 4,800 : 360 = 40 : 3. B = 2,100 : 150 = 14 : 1. C = 6,300 : 500 = 63 : 5.
2
Per one following: A = 13.33, B = 14, C = 12.6.
3
B wins, though C has three times B's followers.

Answer: Account B (14 : 1)

⚡ Benchmark route

Benchmark 14. B is exactly 14. A: 360 × 14 = 5,040 > 4,800, so A is below 14. C: 500 × 14 = 7,000 > 6,300, so C is below too.

⚠️ Adding to both terms is not scaling

3 : 5 plus 5 on each side is 8 : 10 = 4 : 5. Adding the same number drags a ratio towards 1 : 1. Only × and ÷ keep it fixed.

Why can't a ratio tell you the actual numbers?

A ratio is a shape, not a size: 3 : 2 fits 30 and 20 or 450 and 300. You need the total or one real value. Without either, 'cannot be determined' is the honest answer.

🎛️ Try it yourself — change any number

Turn a ratio into real numbers

Cups Kabir sold today Tea (parts) Coffee (parts) Cold drinks (parts, 0 if none)

One part is worth

150

100

250 ÷ (3 + 2) = 50 per part

Tea : coffee = 3 : 2 and 250 cups: one part is 50, so 150 tea, 100 coffee. Make it 1,000 cups: same ratio, four times the cups.

🧭 Decision flow

Can you actually find this ratio?

❓ Are both quantities shares of the same total?

Yes →

Divide the percentages directly. The total cancels.

15% : 12% = 5 : 4

No ↓

❓ Do you know each base, or how they compare?

Yes →

Multiply each share by its own base, then form the ratio.

No →

Cannot be determined.

How does a ratio hide inside a CLAT caselet?

CLAT Quant is now a few caselets. A passage either gives a ratio ("males to females is 2 : 3") or gives percentages and asks for one. Either way: same unit, then simplify. Splitting totals is the next page, dividing in a given ratio.

✍️ Worked example Tricky ⏱ 75 sec

The fest registrations

A fest has 2,400 registrations: 35% for Debate, 25% for Quiz. First-years to others is 3 : 4 in Debate and 5 : 7 in Quiz. Find first-years in Debate : first-years in Quiz.

1
Debate = 35% of 2,400 = 840. First-years = 3/7 × 840 = 360.
2
Quiz = 25% of 2,400 = 600. First-years = 5/12 × 600 = 250.
3
360 : 250, ÷ 10 = 36 : 25. Debate first, as asked.

Answer: 36 : 25

⚡ Skip the total

Skip the 2,400. 35 × 3/7 = 15 and 25 × 5/12 = 125/12. Multiply both by 12: 180 : 125 = 36 : 25.

📊 The data

The fest caselet as a chart

First-yearsOthers

Debate (840) · 3 : 4

360

480

Quiz (600) · 5 : 7

250

350

3 : 4 and 5 : 7 live inside each event. Comparing across events needs real numbers.

📌 Same base? The base cancels

Rent 15% and education 12% of one income is 5 : 4, whatever the income. Different bases? Carry each base along.

Which ratio traps does CLAT set?

🧩 At a glance

Five ways a ratio question catches you

🔁Flipped order

Both orders sit in the options.

🧩Part vs whole

3 : 2 makes girls 2/5, not 2/3.

➕Adding to both

Changes the ratio.

📏Mixed units

Convert before you divide.

❓Different bases

No group sizes, no comparison.

How has CLAT asked ratio basics?

📝 Asked in CLAT 2021 · Q148 Same base

…in the year 2019, he spent 23 per cent of his income on food, 15 per cent on Housing, and 12 per cent on his child's education. For his transport, he spent 10 per cent, and for clothing of his family he spent 10 per cent… also saved 15 per cent of his income…

What was the ratio of the total amount of money spent on housing to that spent on education?

A5:2

B2:5

C4:5

D5:4

Reveal answer + reasoning

Answer: D

Both are shares of the same income, so it cancels. 15 : 12, ÷ 3 = 5 : 4. Time: 10 seconds.

Why the others fail

A — Needs education at 6%; it is 12%.
B — Option A flipped, a decoy.
C — Education : housing, the reverse order.

📝 Asked in CLAT 2024 · Q111 Different bases

…Total number of cars… was 8000. Of these, State 1 had 15% of the total cars in the ratio of 3:4:1 (diesel, petrol and electric); State 2 had 20%… in the ratio of 5:3:2…; State 3 had 30% of the total cars in the ratio of 4:5:3 (diesel, petrol and electric), and; State 4 had 35% of the total cars in the ratio of 7:5:2 (diesel, petrol and electric)…

What is the ratio of diesel cars in State 4 to electric cars in State 3?

A7:3

B3:7

C7:4

D4:7

Reveal answer + reasoning

Answer: A

State 4 = 35% of 8,000 = 2,800; diesel = 7/14 × 2,800 = 1,400. State 3 = 2,400; electric = 3/12 × 2,400 = 600. 1,400 : 600 = 7 : 3. Reading off the terms 7 and 3 works here only by luck: one part is 200 cars in both states. Time: 40 seconds.

Why the others fail

B — Reverse order.
C — Uses State 3 diesel (the 4), the wrong fuel.
D — Wrong fuel and reversed.

📝 Asked in CLAT 2022 · Q150 Ratio inside ratios

…the total number of employees… are 4,500… In marketing, ratio of males to females is 2 : 3 and number of employees engaged in marketing is 20% of the total employment. 12% of the total numbers of workers are running the Hr department and the ratio of males to females in this department is 5 : 1…

What is the ratio of number of males in marketing department to the number of males in Hr department?

A4 : 5

B5 : 4

C7 : 3

D6 : 7

Reveal answer + reasoning

Answer: A

Marketing = 900; males = 2/5 × 900 = 360. HR = 540; males = 5/6 × 540 = 450. 360 : 450 = 4 : 5. Faster: same 4,500 base, so 20 × 2/5 : 12 × 5/6 = 8 : 10. Time: 30 seconds.

Why the others fail

B — Reverse order.
C — Not reachable from the data.
D — Not reachable either; recheck 2/5 and 5/6.

📝 Asked in CLAT 2022 · Q140 Find the missing part first

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. Data regarding students opting for various streams… showed that 25% of the enrolled students opted non-medical and the percentage of girls in Non-medical was 30% of the total number of girls…

What is the ratio among boys and girls for Non-medical?

A3 : 17

B17 : 8

C8 : 17

D17 : 3

Reveal answer + reasoning

Answer: C

Non-medical = 25% of 3,000 = 750. Girls = 30% of 1,700 = 510. Boys = 750 − 510 = 240. 240 : 510, ÷ 30 = 8 : 17. The two percentages have different bases (all students vs all girls), so 25 : 30 means nothing here. Time: 45 seconds.

Why the others fail

A — No step gives it; it borrows the girls' 17 as bait.
B — Girls : boys, the reverse order.
D — The same bait as A, flipped.

Can you beat the ratio myths and quiz?

💥 Myth vs fact

Traps students fall for

🙅 Myth

3 : 5 means 3 and 5 people.

Tap to bust it →

✅ Fact

It means parts. 30 and 50 fit too.

🙅 Myth

Adding the same number keeps the ratio.

Tap to bust it →

✅ Fact

Only × and ÷ do.

🙅 Myth

Boys : girls = 3 : 2 makes girls 2/3 of the class.

Tap to bust it →

✅ Fact

Girls are 2/5 = 40%.

🙅 Myth

You can't take a ratio of percentages without the total.

Tap to bust it →

✅ Fact

If both are shares of the same total, you can: it cancels.

🎯 Quick quiz

Five quick ratio checks

0 / 5

Q1. Simplify 1.5 kg : 600 g.

Q2. Two numbers are in the ratio 3 : 5. Adding 6 to each makes it 3 : 4. The smaller number is?

Q3. Which ratio is the greatest?

A society has 1,200 residents. 40% are students; school : college students = 5 : 3. One in four other residents is a senior citizen.

Q4. College students : senior citizens = ?

Boys : girls is 3 : 2 in Class A and 4 : 5 in Class B.

Q5. Boys in A : boys in B = ?

🎯 Ratio basics in a nutshell

a : b = a/b: parts, not people.
Clean the terms, then divide by the HCF.
Compare with a × d vs b × c.
Part-to-whole = a/(a + b).
No total, no real value: cannot be determined.

📎 Formula card

a : b = a/b; × or ÷ both terms: unchanged.
Compare: a : b > c : d when a × d > b × c.
One part = total ÷ (a + b).
Same base: p% of T : q% of T = p : q.
Inverse b : a; duplicate a² : b²; compound of a : b and c : d is ac : bd.

Frequently asked questions

What is the difference between ratio and proportion?

A ratio compares two quantities, like 3 : 2. A proportion says two ratios are equal, like 3 : 2 = 12 : 8. In CLAT you read ratios off a caselet, then use proportion to scale them to real numbers.

How do you simplify a ratio with decimals or fractions?

Multiply every term by the same number to clear them: 0.4 : 1.25 × 100 is 40 : 125; 2/3 : 3/4 × 12 is 8 : 9. Then divide by the HCF, so 40 : 125 becomes 8 : 25.

How do you compare two ratios quickly?

Cross-multiply. For a : b and c : d, compare a × d with b × c; the bigger product marks the bigger ratio. 3 : 4 against 5 : 7 gives 21 against 20, so 3 : 4 wins.

Does adding the same number to both terms change a ratio?

Yes. Only multiplying or dividing keeps it. 3 : 5 plus 5 each is 8 : 10, or 4 : 5. Age questions use this: two ages in one ratio today sit in a different ratio later.

What is a part-to-whole ratio?

It compares one part with the total, not with another part. If boys to girls is 3 : 2, the class has 5 parts, so boys to class is 3 : 5 and boys are 60%. Reading 3 : 2 as 'girls are two-thirds of the class' is a common slip; they are two-fifths.