📑 On this page
⚡ The short answer
To combine A : B and B : C, make B the same number in both (use the LCM), then read off A : B : C. Formula: a : b and c : d give ac : bc : bd, so A : C = ac : bd. Trap: never add ratio terms across groups; use real counts.
🎬 The 30-second story
The follower fight
1
“I've got 3 followers for every 4 of Zoya's.”
📱
Aarav
Group chat, 11 pm.
2
“Cute. And I've got 6 for every 7 of Meher's.”
📊
Zoya
Zoya adds a second ratio.
3
“So it's Meher 7, me 3? She's beating me more than double!”
🤯
Aarav
Aarav glues the 3 of one ratio to the 7 of the other.
4
“Bhaiya, your 4 and my 6 are both Zoya. Just not the same size.”
🧮
Meher
Zoya is the bridge, written at two zoom levels.
Tara's maths: Make Zoya equal: 9 : 12 and 12 : 14, so Aarav : Zoya : Meher = 9 : 12 : 14. Meher has about 1.56 times Aarav's count, not 2.33 times.
How do you combine two ratios like A : B and B : C?
Every ratio counts in its own private unit. One 'part' in Aarav : Zoya might be 100 followers; in Zoya : Meher, something else. So the 4 and the 6 are both Zoya, in different-sized parts, like 4 metres and 6 feet.
The fix: scale both ratios so the shared person gets the same number. Multiplying both terms by the same number never changes a ratio. Use the LCM of the shared values: LCM(4, 6) = 12. Any common multiple works; the LCM keeps numbers small.
🧮 The formula
Bridge the shared term, then read across
🔗
Aarav : Zoya = 3 : 4
× 3 → 9 : 12
+
🔗
Zoya : Meher = 6 : 7
× 2 → 12 : 14
=
⛓️
A : Z : M = 9 : 12 : 14
Zoya is 12 in both
What is the formula for A : B : C and the compound ratio?
General case: A : B = a : b, B : C = c : d. Skip the LCM hunt: multiply the first ratio by c and the second by b. Now B is bc in both.
| Step | A | B | C |
|---|---|---|---|
| A : B × c | ac | bc | |
| B : C × b | bc | bd | |
| Joined | ac | bc | bd |
| Story: 3 : 4 and 6 : 7 | 18 | 24 | 28 → 9 : 12 : 14 |
→ scroll to see more
📌 A : C is a compound ratio: just multiply
(A/B) × (B/C) = A/C: B cancels like a connecting train. So A : C = ac : bd; for the story, 18 : 28 = 9 : 14. It also works when one quantity is built from two: revenue ratio = price ratio × quantity ratio.
How do combined ratios show up in CLAT-style sums?
✍️ Worked example
CLAT level
⏱ 60 sec
The fest budget with a flipped ratio
Zoya's fest splits ₹1,52,000 among Food, Décor and Sound. Food : Décor = 7 : 4 and Sound : Food = 3 : 5. Find each share.
- 1Food sits second in Sound : Food. Flip it: Food : Sound = 5 : 3.
- 2LCM(7, 5) = 35. Food : Décor = 35 : 20; Food : Sound = 35 : 21.
- 3Food : Décor : Sound = 35 : 20 : 21, total 76 parts.
- 4One part = 1,52,000 ÷ 76 = ₹2,000. Food 35 × 2,000 = ₹70,000; Décor ₹40,000; Sound ₹42,000. They add to ₹1,52,000.
Answer: Food ₹70,000, Décor ₹40,000, Sound ₹42,000
⚡ The exam-hall shortcut
A clean division (1,52,000 ÷ 76) is a good sign. A messy one hints you joined the wrong terms.
🥧 The split
Where the ₹1,52,000 went
- Food₹70,00046.1%
- Sound₹42,00027.6%
- Décor₹40,00026.3%
✍️ Worked example
CLAT level
⏱ 45 sec
Kabir's two phone models
Kabir sells two phone models. Prices are in the ratio 3 : 2, units sold 4 : 5, and total revenue is ₹22 lakh. What did each model earn?
- 1Revenue = price × units: 3 × 4 : 2 × 5 = 12 : 10 = 6 : 5.
- 211 parts = ₹22 lakh, so one part = ₹2 lakh: ₹12 lakh and ₹10 lakh.
Answer: ₹12 lakh and ₹10 lakh (revenue ratio 6 : 5)
⚡ The exam-hall shortcut
Adding terms (3 + 4 : 2 + 5 = 7 : 7) would wrongly say both earned the same. Multiply, never add.
What is the fastest way to combine three or four ratios?
For a chain A : B, B : C, C : D, the zig-zag does it in one pass. Each term is a product of three numbers: take first terms until you reach your letter, then second terms.
✍️ Worked example
Tricky
⏱ 75 sec
Four friends, one pocket-money chain
Pocket money: Aarav : Zoya = 1 : 2, Zoya : Meher = 3 : 4, Meher : Rohan = 5 : 6. Rohan gets ₹1,320 more than Aarav. Meher gets?
- 1Aarav = 1 × 3 × 5 = 15; Zoya = 2 × 3 × 5 = 30; Meher = 2 × 4 × 5 = 40; Rohan = 2 × 4 × 6 = 48.
- 2Rohan − Aarav = 33 parts = ₹1,320, so one part = ₹40.
- 3Meher = 40 × 40 = ₹1,600 (Aarav ₹600, Zoya ₹1,200, Rohan ₹1,920).
Answer: Meher gets ₹1,600
⚡ The exam-hall shortcut
Given a gap, subtract parts. You never need the full sum.
🎛️ Try it yourself — change any number
Join any two ratios
A : B : C
9 : 12 : 14
Make B equal: A : B = 18 : 24, B : C = 24 : 28 → 9 : 12 : 14
Starts on the follower fight. Try 2, 3, 4, 5 (8 : 12 : 15).
💡 Let the options do half the work
Test one link per option: in 9 : 12 : 14, the first two terms must reduce to 3 : 4.
How do you find the overall ratio when groups have different ratios?
CLAT's favourite: several groups, each with its own ratio, and a question about everyone together. Ratios hide group sizes, so turn each group into real counts, add, then form the ratio. Mini caselet: X, Y and Z send 120, 90 and 150 students to a debate fest, with boys : girls of 7 : 5, 1 : 2 and 3 : 2.
| College | Students | Boys : Girls | Boys, Girls |
|---|---|---|---|
| X | 120 | 7 : 5 (12 parts of 10) | 70, 50 |
| Y | 90 | 1 : 2 (3 parts of 30) | 30, 60 |
| Z | 150 | 3 : 2 (5 parts of 30) | 90, 60 |
| All | 360 | 190 : 170 = 19 : 17 | 190, 170 |
→ scroll to see more
📊 The data
Debate fest: boys and girls by college
BoysGirls
X
70
50
Y
30
60
Z
90
60
All three · 19 : 17
190
170
Adding ratio terms gives 11 : 9. Wrong: it's 19 : 17.
Follow-ups become one-liners: girls from Y : boys from Z = 60 : 90 = 2 : 3; girls' share = 170/360, about 47.2%.
What traps does CLAT set with combined ratios?
🧭 Decision flow
Can you combine these ratios?
❓ Merging groups into one total?
Yes →
Real counts per group, add, then form the ratio.
No ↓
❓ Do the ratios share a term (B in A : B, B : C)?
No →
Cannot be determined without another link.
Yes ↓
❓ Is the shared term already equal?
Yes →
Read A : B : C straight across.
No →
Scale to the LCM (or zig-zag), then read across.
⚠️ Percentages with different bases
'56% of rural' and '40% of urban' sit on different bases: multiply by each base before comparing. '% of the total' means a shared base. Ask 'of what?' twice.
📝 Asked in CLAT 2022
· Q148
Overall ratio from department ratios
In an organization, the total number of employees working in various departments viz. IT, Marketing, Purchase, HR, Accounts and Production are 4,500. … 18 percent of total number of employees work in IT department and ratio of males to females in IT department is 2 : 1. In Marketing, ratio of males to females is 2 : 3 and number of employees engaged in Marketing is 20% … 12% … are running the HR department and the ratio of males to females in this department is 5 : 1. The fraction of male to females in Production department is 3 : 2 and … this department is 15% of the total workforce. … Purchase and Accounts department is 24% and 11% respectively … Gender ratio … in Purchase department is 1 : 1 and in Accounts is 1 : 2.
What is the ratio of total number of males to total number of females working in all the departments put together?
A63 : 41
B19 : 27
C41 : 34
D34 : 41
Reveal answer + reasoning
Answer: C
Merging groups, so use counts. Work in % of staff:IT 18 → 12 M, 6 F. Marketing 20 → 8, 12. HR 12 → 10, 2. Production 15 → 9, 6. Purchase 24 → 12, 12. Accounts 11 → 11/3, 22/3.
Males 54⅔, females 45⅓. × 3: 164 : 136 = 41 : 34 (2,460 and 2,040 people).
Eliminate first: IT, HR and Production lean male, so the ratio is above 1; B and D die. About 90 seconds.
Why the others fail
- A — About 1.54, far too male-heavy; the true ratio is about 1.21.
- B — Below 1, so females would outnumber males.
- D — Flipped: females to males.
📝 Asked in CLAT 2023
· Q140
Compound ratio across three bases
[Data added in the previous question] … In 2019-20, 60 percent of all males aged 15 years and more have regular salaried and self-employed jobs while 19 percent of all similarly aged females get regular and self-employment.
In 2019-20, if the number of males aged 15 years and more is 76% of the total male population and the number of females aged 15 years and more is 72% of the total female population and the total male population is 1.05 times the total female population, what is the ratio of females to males aged 15 years and more that have regular salaried and self-employed jobs?
A2 : 7
B3 : 10
C5 : 9
D1 : 3
Reveal answer + reasoning
Answer: A
Compound the three ratios: F : M = (19/60) × (72/76) × (100/105).Cancel: 19/76 = 1/4, 72/60 = 6/5, 100/105 = 20/21. So (1/4) × (6/5) × (20/21) = 120/420 = 2/7.
Check with 100 females: 19% of 72 = 13.68; males 60% of 79.8 = 47.88; 13.68 : 47.88 = 2 : 7. About 60 seconds.
Why the others fail
- B — Forgets the 1.05 males per female.
- C — Far too high: 19% is under a third of 60%.
- D — Roughly 19 : 60, the job rates alone.
📝 Asked in CLAT 2024
· Q120
Check the base before compounding
A survey was conducted about the population of a particular region having working population of three lacs … Self-employment … is more prevalent in rural areas (56% of the rural population) than in urban areas (40% of the urban population). Rural population was 48% of the total population. …
If 60% of the total working population of the region were self-employed in rural areas and 40% of total population were self-employed in urban areas, then what is the ratio of rural self-employed to urban self-employed?
A2:3
B3:2
C13:18
D18:13
Reveal answer + reasoning
Answer: B
Both percentages are of the total, so the base is shared: 60 : 40 = 3 : 2 (1,80,000 and 1,20,000). About 20 seconds.The trap: treat them as shares of the rural (48%) and urban (52%) groups and you get 60 × 48 : 40 × 52 = 18 : 13, option D. (Same set, Q116: urban : rural = 52 : 48 = 13 : 12.)
Why the others fail
- A — Flipped.
- C — The trap, flipped.
- D — Uses the wrong base.
Quick check: can you combine ratios now?
💥 Myth vs fact
Myths that cost marks
🙅 Myth
Join A : B and B : C by writing them side by side.
Tap to bust it →
✅ Fact
Only if B is already equal. Otherwise scale first.
🙅 Myth
Overall ratio of groups = add the ratio terms.
Tap to bust it →
✅ Fact
Works only by luck. Real counts first, then add.
🙅 Myth
A : B and C : D give A : D.
Tap to bust it →
✅ Fact
No shared term, no bridge: cannot be determined.
🙅 Myth
A merged group ratio can land anywhere.
Tap to bust it →
✅ Fact
It sits between the group ratios. Options outside that range are dead.
🎯 Quick quiz
Five chains to join
0 / 5
Day passes : weekend passes = 4 : 5; weekend : VIP = 2 : 3.
Q1. Day : weekend : VIP?
LCM(5, 2) = 10: 8 : 10 and 10 : 15.Maths : English = 2 : 3 and Maths : GK = 4 : 5.
Q2. English : GK?
Make Maths 4: 4 : 6 and 4 : 5.Section X (30 students) has boys : girls = 1 : 2. Section Y has 3 : 1; its size isn't given.
Q3. Boys : girls overall?
Y = 20 gives 1 : 1; Y = 40 gives 4 : 3. The answer moves.Two biscuit packs: prices 5 : 4, units sold 3 : 5.
Q4. Revenue ratio?
15 : 20 = 3 : 4. D adds instead of multiplying.60% of a town are adults. 25% of adults and 10% of minors use an app.
Q5. Adult users : minor users?
25% of 60 : 10% of 40 = 15 : 4. A ignores the bases.🎯 Combining ratios in a nutshell
- A shared term must be equal before two ratios join.
- LCM, or zig-zag: a : b and c : d give ac : bc : bd.
- A : C alone is the compound ratio ac : bd.
- Merging groups? Real counts first; the answer sits between the group ratios.
- No shared term: cannot be determined.
📎 Formula card
- Join two: a : b, c : d → ac : bc : bd
- Compound ratio: A : C = ac : bd
- Join four: a : b, c : d, e : f → ace : bce : bde : bdf
- Groups: total counts : total counts
- Percent of a percent: group share × % within group
Frequently asked questions
How do you combine ratios A:B and B:C?
Make B the same number in both. Take the LCM of B's two values and scale each ratio to it. For 3 : 4 and 6 : 7 the LCM is 12, giving 9 : 12 and 12 : 14, so A : B : C = 9 : 12 : 14. Or multiply crosswise: ac : bc : bd.
What is a compound ratio?
The product of ratios: multiply the first terms together and the second terms together. The compound of 3 : 4 and 6 : 7 is 18 : 28, or 9 : 14. It gives A : C straight from A : B and B : C, and price ratio times quantity ratio gives the revenue ratio.
Can you add the ratios of two groups to get the overall ratio?
No. Adding terms ignores group sizes. Turn each group into real counts, add them, then form the ratio. If a group's size is missing, the overall ratio usually cannot be determined. The answer always lies between the group ratios.
How do you combine three ratios A:B, B:C and C:D?
Zig-zag. For a : b, c : d and e : f, the terms are ace, bce, bde and bdf: first terms until you reach the letter, then second terms. So 1 : 2, 3 : 4 and 5 : 6 give 15 : 30 : 40 : 48.
What if the common term is in a different position in each ratio?
Rearrange first so the shared term lines up. If A : B = 2 : 3 and C : A = 5 : 4, rewrite the second as A : C = 4 : 5. Make A equal (LCM 4): A : B = 4 : 6, so A : B : C = 4 : 6 : 5.
Keep going
← Previous topic
Dividing a Quantity in a Given Ratio
The parts method: split any total, from a cab bill to a CLAT caselet
Next topic →
Proportion, Third and Mean Proportional
Fourth, third and mean proportional from one cross rule
📚
Part of the chapter
Ratio & Proportion for CLAT Quantitative Techniques
See how this topic fits the whole of Ratio & Proportion →
Connected topics in other chapters
Ratio Basics: Simplifying and Comparing Ratios
Scaling a ratio up or down is the move that makes bridging possible.
Dividing a Quantity in a Given Ratio
Once A : B : C is built, the parts method turns it into rupees.
Partnership: Sharing Profit by Capital × Time
Capital × time is a compound ratio in disguise.
Weighted Average
Merging group ratios is the same idea as a weighted average: size matters.
Caselet DI: Turning a CLAT Quant Passage into a Table
The department-by-department table method used in the 2022 question.
Every topic in Ratio & Proportion
- 1.Ratio Basics: Simplifying and Comparing Ratios
- 2.Dividing a Quantity in a Given Ratio
- 3.Combining Ratios: A:B, B:C and Overall Ratios (you're here)
- 4.Proportion, Third and Mean Proportional
- 5.Direct and Inverse Proportion
- 6.The Unitary Method
- 7.Partnership: Sharing Profit by Capital × Time
- 8.Problems on Ages: The Constant-Gap Trick