📑 On this page
⚡ The short answer
To divide a quantity in a given ratio, add the terms to get the number of equal parts, divide the total by that sum to get one part, then multiply each term by it. Share of A = Total × a/(a + b + c). The trap: apply a ratio only to the group it describes, never the grand total.
🎬 The 30-second story
The 2 a.m. cab split
1
“₹840 for the cab. Three of us, ₹280 each. Done.”
🚕
Aarav
Three friends share one cab home after the fest.
2
“Bhai, I got off after 1 km!”
📍
Rohan
Rohan rode 1 km, Aarav 2, Meher 4.
3
“Fine. Split it by kilometres: 4 : 2 : 1.”
🧮
Meher
She lives farthest, so she offers to pay most.
4
“But how do you split ₹840 into 4, 2 and 1?”
😵
Aarav
CLAT's question, minus the cab.
Tara's maths: 4 + 2 + 1 = 7 parts. One part = ₹840 ÷ 7 = ₹120. Meher pays ₹480, Aarav ₹240, Rohan ₹120, which adds back to ₹840. Rohan saves ₹160 on Aarav's 'equal' plan.
What does it mean to divide something in a ratio?
A ratio is a recipe, not a count. 4 : 2 : 1 doesn't mean Meher pays ₹4. It means: chop the bill into equal blocks and hand out 4, 2 and 1. The only unknown is how big one block is.
🟦 Picture the percent
Same 100 squares, cut by two different recipes
Split 3 : 2
5 parts: one part = 20
A: 3 partsB: 2 parts
Split 5 : 3 : 2
10 parts: one part = 10
A: 5 partsB: 3 partsC: 2 parts
🧮 The formula
The cab bill, as blocks
🟦
Meher: 4 parts
+
🟩
Aarav: 2 parts
+
🟨
Rohan: 1 part
=
🧾
7 parts = ₹840
so 1 part = ₹120
The ratio alone never gives the money: 4 : 2 : 1 fits a ₹70 auto fare and a ₹7,000 airport cab alike. Ratio gives the shape; the total gives the size.
What is the formula for dividing in a given ratio?
Each share is a fraction of the whole: its own parts over all the parts. Meher has 4 of the 7 parts, so she pays 4/7 of ₹840 = ₹480. In general, if T is split in a : b : c, then A's share = T × a/(a + b + c). That's the cab story in algebra, not a new formula.
- 1
Add the termsa + b + c = number of equal parts. For 5 : 4 : 3, that's 12.
- 2
Find one partTotal ÷ sum of terms. This one number unlocks every share.
- 3
Multiply only what's askedShare = its term × one part.
- 4
Check the sumShares must add back to the total.
📌 One part is the master key
A caselet asks four or five questions on the same split. Find one part once, write it beside the group in your rough work, and every later question is a single multiplication.
How do you divide a quantity in a ratio? Worked examples
✍️ Worked example
Warm-up
⏱ 20 sec
Pocket money: save vs spend
Meher splits her ₹2,400 monthly allowance between savings and spending in 3 : 5. How much does she save?
- 1Parts = 3 + 5 = 8.
- 2One part = 2,400 ÷ 8 = ₹300.
- 3Savings = 3 × 300 = ₹900; spending = ₹1,500. Sum: 2,400.
Answer: Meher saves ₹900.
⚡ The exam-hall shortcut
3 parts out of 8 is 3/8. Eighth of 2,400 is 300, three of them is 900.
✍️ Worked example
CLAT level
⏱ 35 sec
The fest budget, three ways
A ₹96,000 fest budget is split among Cultural, Sports and Tech in 5 : 4 : 3. How much more does Cultural get than Tech?
- 1Parts = 5 + 4 + 3 = 12; one part = 96,000 ÷ 12 = ₹8,000.
- 2Cultural = 5 × 8,000 = ₹40,000; Tech = 3 × 8,000 = ₹24,000.
- 3Difference = ₹16,000.
Answer: Cultural gets ₹16,000 more.
⚡ The exam-hall shortcut
The gap is 5 − 3 = 2 parts. 2 × 8,000 = ₹16,000. You never need the two shares separately.
✍️ Worked example
Tricky
⏱ 40 sec
No total, only a difference
Rohan's and Aarav's follower counts are in the ratio 7 : 4. Rohan has 360 more followers than Aarav. How many followers do they have together?
- 1The 360 gap is 7 − 4 = 3 parts.
- 2One part = 360 ÷ 3 = 120.
- 3Together = 11 × 120 = 1,320 (Rohan 840, Aarav 480).
Answer: 1,320 followers together.
⚡ The exam-hall shortcut
Any real number works: divide it by its own number of parts. Difference ÷ gap in terms, or one share ÷ its term.
What is the fastest way to split a total in a ratio?
⚔️ Side by side
Slow route vs exam-hall route
🐢Slow route
Every share, every time
- •Computes every share, even when one is asked
- •Redoes the split for each question
⚡Fast route
One part, then multiply
- •Finds one part once per group
- •Uses the gap in terms for 'how much more'
VS
| Test | Slow route | Fast route |
|---|---|---|
| 2024 caselet, State 1 | 1,200 × 3/8, then redo for petrol | 1,200 ÷ 8 = 150, reuse it |
| Time per question | 60–75 sec | 20–30 sec |
Two habits make it quicker. When the sum of terms divides the total cleanly (8 into 1,200), the numbers were built for the parts method. And options that count people or cars must be whole multiples of one part, which often kills two options before you multiply.
💡 The whole-number sanity check
Counting cars or people and one part comes out as 571.4? Stop: you've applied the ratio to the wrong total. State 4's 7 : 5 : 2 on all 8,000 cars gives exactly that nonsense.
🎛️ Try it yourself — change any number
Split any total in a ratio
One part is worth
8,000
A
40,000
B
32,000
C
24,000
96,000 ÷ (5 + 4 + 3) = 8,000 per part
Default: ₹96,000 in 5 : 4 : 3 gives ₹8,000 per part. Now try 2,800 in 7 : 5 : 2: one part is 200.
How does dividing in a ratio hide inside a CLAT caselet?
CLAT rarely says 'divide 2,400 in 3 : 2'. It gives a grand total, then each group's percentage share, then a ratio inside each group: two splits stacked, and the order matters.
🕒 Timeline
The two-layer split: a coaching centre with 2,400 students
-
1
Layer 1Percentage → group total2,400 students: Morning 25% = 600, Evening 40% = 960, Weekend 35% = 840.
-
2
Layer 2Ratio → one partGirls : boys = 3 : 2, 1 : 1, 5 : 9. One part = 120, 480, 60.
-
3
AnswerMultiply outGirls 360, 480, 300; boys 240, 480, 540.
📊 The data
Girls and boys by batch (from the caselet)
GirlsBoys
Morning
360
240
Evening
480
480
Weekend
300
540
Weekend is the trap: 5 : 9 adds to 14, so one part is 60.
✍️ Worked example
CLAT level
⏱ 45 sec
The caselet question
Using the coaching-centre caselet, how many more boys than girls are there in the whole centre?
- 1Boys = 240 + 480 + 540 = 1,260.
- 2Girls = 360 + 480 + 300 = 1,140.
- 3Difference = 1,260 − 1,140 = 120.
Answer: 120 more boys.
⚡ The exam-hall shortcut
Use gaps: Morning girls lead by 1 part (120), Evening is level, Weekend boys lead by 4 parts (240). Net: 120 more boys.
What traps does CLAT set when you divide in a ratio?
🧭 Decision flow
What real number do you have? Pick your route
❓ Do you know the total of this exact group (not the grand total)?
Yes →
One part = group total ÷ sum of terms
No ↓
❓ Do you know the difference between two shares?
Yes →
One part = difference ÷ gap in terms
No ↓
❓ Do you know any one share?
Yes →
One part = that share ÷ its own term
No ↓
❓ Does the question ask only for a fraction or ratio?
Yes →
Answer from the terms alone: B's share of 5 : 4 : 3 is 1/3
No →
Cannot be determined
A ratio with no real number has no size.
⚠️ The wrong-total trap
'State 4 had 35% of the cars in the ratio 7 : 5 : 2' means 7 : 5 : 2 splits State 4's 2,800 cars, not all 8,000. It's the commonest way to lose a CLAT ratio mark, and the options reward it with a plausible number. Also read the order: 'males to females 1 : 2' gives females the 2.
How did CLAT ask dividing in a ratio?
📝 Asked in CLAT 2024
· Q109
Percentage, then ratio
… Total number of cars for which data was collected was 8000. Of these, State 1 had 15% of the total cars in the ratio of 3:4:1 (diesel, petrol and electric); … State 4 had 35% of the total cars in the ratio of 7:5:2 (diesel, petrol and electric). Based on the above information, answer the following questions.
If 45% of the electric cars in State 4 are air conditioned (AC) and remaining are non-AC, what is the number of non-AC cars?
A380
B240
C220
D180
Reveal answer + reasoning
Answer: C
State 4 = 35% of 8,000 = 2,800. 7 + 5 + 2 = 14 parts, so one part = 200 and electric = 2 × 200 = 400. Non-AC = 55% of 400 = 220. Answer C, in about 40 seconds.
Why the others fail
- A — 380 is 95% of 400: no correct step gives it.
- B — 240 is 60% of 400, a wrong remainder.
- D — 180 is 45% of 400: the AC cars, the opposite of what's asked.
📝 Asked in CLAT 2024
· Q113
Two states, two splits
… Total number of cars for which data was collected was 8000. Of these, State 1 had 15% of the total cars in the ratio of 3:4:1 (diesel, petrol and electric); … State 3 had 30% of the total cars in the ratio of 4:5:3 (diesel, petrol and electric) …
What is the difference between number of petrol cars in State 3 and diesel cars in State 1?
A350
B400
C500
D550
Reveal answer + reasoning
Answer: D
State 3 = 30% of 8,000 = 2,400; 12 parts, one part = 200; petrol = 5 × 200 = 1,000.State 1 = 15% of 8,000 = 1,200; 8 parts, one part = 150; diesel = 3 × 150 = 450.
Difference = 550. Answer D, in about 50 seconds. Each state needs its own one-part value.
Why the others fail
- A — 350 = State 3 diesel (800) − 450. Wrong fuel.
- B — 400 = 1,000 − State 1 petrol (600). Wrong fuel.
- C — 500 matches no pairing; it's a near-miss decoy.
📝 Asked in CLAT 2022
· Q146
Department split
In an organization, the total number of employees working in various departments viz. IT, Marketing, Purchase, HR, Accounts and Production are 4,500. … 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. … The number of persons occupied in Purchase and Accounts department is 24% and 11% respectively of the total number of workers. Gender ratio (ratio of males to females) in Purchase department is 1 : 1 and in Accounts is 1 : 2.
How many females are employed in Purchase department?
A450
B540
C495
D595
Reveal answer + reasoning
Answer: B
Purchase = 24% of 4,500 = 1,080. 1 : 1 is 2 parts, so one part = 540. Females = 540. Answer B, in about 25 seconds.
Why the others fail
- A — 450 is HR males (540 × 5/6). Wrong department.
- C — 495 is the whole Accounts department, unsplit.
- D — 595 matches no group; it's a decoy.
💥 Myth vs fact
Myth vs fact: dividing in a ratio
🙅 Myth
The biggest term always gets more than half.
Tap to bust it →
✅ Fact
In 5 : 4 : 3, the 5 gets 5/12, less than half.
🙅 Myth
1/2 : 1/3 is the same as 2 : 3.
Tap to bust it →
✅ Fact
Multiply by 6: it's 3 : 2.
🙅 Myth
A group's ratio applies to the grand total.
Tap to bust it →
✅ Fact
Find the group total from its percentage first, then split.
🙅 Myth
No total means 'cannot be determined'.
Tap to bust it →
✅ Fact
A difference or one known share gives one part, and a fraction-of-the-whole question needs no number.
Can you divide in a ratio under exam pressure?
🎯 Quick quiz
Five quick splits
0 / 5
Q1. Two sisters share ₹1,350 in the ratio 4 : 5. How much does the elder, with the 4, get?
9 parts, one part = 150. Elder = 4 × 150 = ₹600. ₹750 is the younger sister's.Prize money is split among Aarav, Zoya and Meher in the ratio 3 : 4 : 5. No amount is given.
Q2. Which of these can be stated about Zoya's share?
No rupee figure is given, so no amount can be found. But 4 parts of 12 is exactly one-third, so C holds.Q3. Two accounts have followers in the ratio 9 : 5, and the first has 1,200 more. How many followers do they have together?
Gap = 4 parts = 1,200, so one part = 300. Together = 14 × 300 = 4,200.Q4. ₹4,800 is divided between two people in the ratio 1/3 : 1/5. What is the smaller share?
Multiply by 15: 5 : 3. One part = 4,800 ÷ 8 = 600. Smaller = ₹1,800. ₹1,920 comes from splitting in 2 : 3.A club has 1,500 members; 40% are juniors, and juniors' girls : boys is 7 : 5.
Q5. How many junior boys are there?
Juniors = 600; one part = 50; boys = 250. 625 splits all 1,500 (wrong total); 350 is junior girls.🎯 Dividing in a ratio in a nutshell
- A ratio is equal parts; the total sets the size of one part.
- One part = total ÷ sum of terms; share = term × one part.
- Given a difference or one share? Divide it by its parts.
- Fraction or inverse ratios: clear to whole numbers first.
- Caselets: percentage first, ratio second.
📎 Formula card
- One part = T ÷ (a + b + c); A = T × a/(a + b + c).
- Difference D between A and B → one part = D ÷ (a − b).
- Known share S of A → one part = S ÷ a.
- Inverse of a : b : c = bc : ac : ab.
- 1/2 : 1/3 : 1/4 = 6 : 4 : 3.
- Caselet: group = % × grand total, then split.
- Check: shares add back to the total.
Frequently asked questions
How do you divide a number in a given ratio?
Add the ratio terms to get the number of equal parts, divide the number by that sum to get one part, then multiply each term by one part. To split 2,400 in 3 : 5, there are 8 parts of 300, so the shares are 900 and 1,500.
How do you divide money in the ratio 1/2 : 1/3 : 1/4?
Multiply each fraction by 12, the LCM of 2, 3 and 4, to get 6 : 4 : 3, which is 13 parts. For ₹1,300, one part is ₹100, so the shares are ₹600, ₹400 and ₹300. Splitting in 2 : 3 : 4 would reverse the order.
How do you find the total when only the difference between two shares is given?
The difference equals the gap between the two terms. If A : B is 7 : 4 and A has 360 more, the gap is 3 parts, so one part is 120 and the total is 11 × 120 = 1,320. A known share works the same way: divide it by its own term.
What does dividing in the inverse ratio mean?
The bigger number gets the smaller share. For the inverse ratio of 2 : 3 : 4, flip each term to 1/2 : 1/3 : 1/4, clear the fractions to get 6 : 4 : 3, then use the parts method. Prizes split by time taken work like this.
Why do CLAT caselets give a percentage and a ratio together?
It tests whether you apply each number to the right total. The percentage gives a group's share of the grand total; the ratio splits only that group. In CLAT 2024, State 4 had 35% of 8,000 cars, or 2,800, and only those were split 7 : 5 : 2.
Keep going
← Previous topic
Ratio Basics: Simplifying and Comparing Ratios
What a ratio really says, how to simplify it and compare two fast
Next topic →
Combining Ratios: A:B, B:C and Overall Ratios
Join A:B and B:C into A:B:C, and merge group ratios without traps
📚
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
Clean up a ratio before you split with it.
Combining Ratios: A:B, B:C and Overall Ratios
The next step: CLAT splits each group, then asks for the overall ratio.
Partnership: Sharing Profit by Capital × Time
Profit sharing is dividing in a ratio with a business costume on.
Caselet DI: Turning a CLAT Quant Passage into a Table
Percentage of the total first, ratio second: the two-layer caselet.
Budgets and Pie Charts: Percentage Share
A pie chart is a total divided in a ratio that adds up to 100.
Every topic in Ratio & Proportion
- 1.Ratio Basics: Simplifying and Comparing Ratios
- 2.Dividing a Quantity in a Given Ratio (you're here)
- 3.Combining Ratios: A:B, B:C and Overall Ratios
- 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