Lawyer Hatch Lawyer Hatch
Home/ Quantitative Techniques/ Ratio & Proportion/ Partnership
📚 Part of: Ratio & Proportion guide

Partnership: Sharing Profit by Capital × Time

Money that sits in the business longer earns more. Multiply capital by months, then split the profit like any other ratio.

RR ✔ Reviewed by Ravi Raj Singh · BTech (Computer Science); MA English, NET-qualified
3
CLAT-style caselet Qs
4
worked examples
1
live calculator
10 min
read
Practise Ratio & Proportion drills →
📑 On this page
⚡ The short answer
In a partnership, profit is shared in the ratio of capital × time: C1×T1 : C2×T2. Same period for everyone? Time cancels and the ratio is just the capitals. Then split the profit by the parts method. The trap: 'joined after 4 months' means 8 months of investment, not 4.
🎬 The 30-second story
The cold-coffee cart fight
1
“₹40,000 in the cart from day one. January to December.”
🥤
Kabir
Kabir starts a cold-coffee cart.
2
“I came in May, but with ₹60,000. Bigger cheque, bigger share.”
💸
Rohan
Rohan joins after 4 months to fund a second cart.
3
“Your money missed the whole summer rush!”
📅
Kabir
Year-end profit: ₹54,000. Rohan wants 60%.
4
“So who's right? Capital or calendar?”
🧮
Rohan
Both. That's the point.
Tara's maths: Count rupee-months. Kabir: 40,000 × 12 = 4,80,000. Rohan: 60,000 × 8 = 4,80,000. Ratio 1 : 1, so ₹27,000 each. Rohan's 60% plan would have paid him ₹32,400 for money that sat idle for a third of the year.

How is profit shared in a partnership, and why capital × time?

A business rents money. ₹1 kept in it for one month is one unit of help: a rupee-month. Profit is the rent, paid per unit. Like hiring cycles: two cycles for three days and three for two days are both six cycle-days. Only the total units count.

🧮 The formula
One partner's contribution, as a single number
💰
Capital
₹40,000
×
📅
Months it stayed
12
=
🧱
4,80,000 rupee-months
Kabir's units of help
🟦 Picture the percent
The same ₹54,000, split two ways
Capital only (wrong)
Kabir ₹21,600 · Rohan ₹32,400
Kabir 40%Rohan 60%
Capital × time (right)
₹27,000 each
Kabir 50%Rohan 50%

What is the partnership profit sharing formula?

Turn each partner into one product, then split: A : B : C = C1T1 : C2T2 : C3T3, and A's share = Profit × C1T1 ÷ (sum of products). A loss follows the same ratio. It's dividing in a ratio after one multiplication.

⚔️ Side by side
Simple vs compound partnership
🤝Simple
Everyone in for the same time
  • •Time cancels
  • •Profit ratio = capital ratio
⏳Compound
Different months, or capital changes
  • •Capital × its own months
  • •Profit ratio = ratio of products
TestSimpleCompound
Example₹30k and ₹20k, full year → 3 : 2₹10k × 12 vs ₹15k × 8 → 1 : 1
CLAT tellNo months mentioned'joined after', 'left', 'withdrew'
📌 Three unknowns, one rule
Profit ∝ capital × time, so any two ratios give the third. Time ratio = profit ratio ÷ capital ratio, term by term; capital ratio = profit ratio ÷ time ratio. CLAT likes the reverse version.

How do you calculate each partner's share? Worked examples

✍️ Worked example Warm-up ⏱ 20 sec
The fest bracelet stall
Meher and Zoya run a bracelet stall for one fest weekend. Meher puts in ₹1,500 and Zoya ₹2,500. The stall makes a profit of ₹1,200. What is Meher's share?
  1. 1
    Same weekend, so time cancels: 1,500 : 2,500 = 3 : 5.
  2. 2
    8 parts; one part = 1,200 ÷ 8 = ₹150.
  3. 3
    Meher = 3 × 150 = ₹450; Zoya ₹750. Sum: 1,200.
Answer: Meher gets ₹450.
⚡ The exam-hall shortcut
Strip the zeros: 15 : 25 = 3 : 5. Meher's slice is 3/8 of 1,200.
✍️ Worked example CLAT level ⏱ 40 sec
Three friends, three calendars
Aarav, Zoya and Rohan start a cloud kitchen: Aarav ₹30,000 for 12 months, Zoya ₹45,000 for 8 months, Rohan ₹20,000 for 9 months. Profit: ₹75,000. Rohan's share?
  1. 1
    In thousands: 30 × 12 = 360; 45 × 8 = 360; 20 × 9 = 180.
  2. 2
    360 : 360 : 180 = 2 : 2 : 1.
  3. 3
    5 parts; one part = 75,000 ÷ 5 = ₹15,000. Rohan has 1 part.
Answer: Rohan gets ₹15,000 (Aarav and Zoya ₹30,000 each).
⚡ The exam-hall shortcut
Zoya brought 1.5× Aarav's money for 2/3 of his time: 1.5 × 2/3 = 1, so they tie without multiplying.
✍️ Worked example Tricky ⏱ 60 sec
The repair shop with a mid-year withdrawal
Kabir opens a phone-repair shop on 1 January with ₹60,000. Aarav joins on 1 April with ₹80,000. On 1 October, Kabir withdraws ₹20,000. Profit: ₹69,000. Each one's share?
  1. 1
    Kabir has two slabs: ₹60,000 for Jan–Sep (9 months), ₹40,000 for Oct–Dec (3 months).
  2. 2
    Kabir = 60 × 9 + 40 × 3 = 660 (thousand rupee-months). Aarav = 80 × 9 = 720.
  3. 3
    660 : 720 = 11 : 12; 23 parts; one part = 69,000 ÷ 23 = ₹3,000.
Answer: Kabir ₹33,000, Aarav ₹36,000.
⚡ The exam-hall shortcut
Mark where the money changes on a 12-month line and add one product per slab.
✍️ Worked example Tricky ⏱ 45 sec
Working backwards: when did Rohan join?
Zoya invests ₹24,000 for the whole year; Rohan invests ₹36,000 but joins later. Profit is shared 2 : 1 in Zoya's favour. After how many months did Rohan join?
  1. 1
    Zoya = 24 × 12 = 288; Rohan = 36 × t.
  2. 2
    288 : 36t = 2 : 1, so 36t = 144 and t = 4 months.
  3. 3
    His money worked 4 months, so he joined after 12 − 4 = 8 months.
Answer: Rohan joined after 8 months.
⚡ Ratio-only route
Time ratio = profit ÷ capital = 2/24 : 1/36 = 3 : 1. Zoya's 12 months is 3 parts, so Rohan's is 4. Then answer what's asked: 12 − 4 = 8.

What is the fastest way to solve partnership questions?

Never multiply 60,000 × 8 in full. Partnership is a compound ratio: simplify capitals (40 : 60 = 2 : 3), simplify months (12 : 8 = 3 : 2), multiply term by term: 6 : 6 = 1 : 1. No zeros, done in your head.

🧭 Decision flow
Which ratio do I use?
❓ Is there a salary, fee or commission for one partner?
'working partner', 'fee'
Yes →
Pay it off the top first, then share only the remainder.
No ↓
❓ Did every partner's money stay for the same period?
Yes →
Profit ratio = capital ratio. Time cancels.
No ↓
❓ Did anyone add or withdraw money mid-way?
Yes →
Split that partner into slabs; add capital × months per slab.
No →
Profit ratio = C1T1 : C2T2 : C3T3.
💡 Estimate who wins before you calculate
'Who gets the most?' needs no profit figure. Compare products in thousands: 120 × 12 = 1,440 beats 150 × 6 = 900. The biggest cheque is often the trap option.
🎛️ Try it yourself — change any number
Split any partnership profit
Ratio A : B
1 : 1
A's share
27,000
B's share
27,000
40,000×12 : 60,000×8 = 1 : 1
Default: the coffee cart, ₹27,000 each. Set Rohan's months to 12: the split becomes 2 : 3 and he gets ₹32,400.

How does partnership hide inside a CLAT caselet?

CLAT won't say 'find capital × time'. It writes a paragraph about friends opening a café, drops in amounts and dates, and asks four questions. Turn it into a table before touching an option.

Zoya, Aarav and Rohan open a summer café. Zoya puts in ₹1,20,000 for all 12 months. Aarav brings ₹90,000 but joins 4 months after opening. Rohan brings ₹1,50,000 but withdraws it after 6 months. The year's profit is ₹3,40,000.

— A CLAT-style caselet (written for this page)
PartnerCapital × monthsProduct (₹ thousand)Share
Zoya120 × 121,440 → 8₹1,60,000
Aarav90 × 8720 → 4₹80,000
Rohan150 × 6900 → 5₹1,00,000
Total17 parts₹3,40,000 (₹20,000 a part)
→ scroll to see more
📊 The data
Money put in vs profit taken out (₹ thousand)
Capital investedProfit share
Zoya · 12 months
₹120k
₹160k
Aarav · 8 months
₹90k
₹80k
Rohan · 6 months
₹150k
₹100k

Rohan invested the most but takes less than Zoya. On capital alone he would have claimed about ₹1,41,667; time cut that to ₹1,00,000.

Now every follow-up is one line. Zoya's share as a percentage of profit? 8/17 ≈ 47.1%. Rohan's lead over Aarav? 1 part = ₹20,000.

What traps does CLAT set in partnership questions?

Phrase in the passageMonths to use (12-month year)Why
'joined after 4 months'812 − 4: no money for the first 4
'left after 4 months'4Money worked until it left
'joined at the start of the 4th month'9Months 4 to 12 inclusive
'withdrew ₹X after 6 months'6 + 6, two slabsFull capital × 6, reduced × 6
→ scroll to see more
⚠️ The salary comes off the top
Aarav runs the shop and takes 10% of a ₹50,000 profit as salary; capitals are 3 : 2 in his favour. Salary ₹5,000; only ₹45,000 splits 3 : 2, so Aarav gets ₹27,000 + ₹5,000 = ₹32,000 and the other ₹18,000. Splitting all ₹50,000 first pays out ₹55,000.

How could CLAT ask partnership questions?

No CLAT UG paper from 2018 to 2025 has a pure partnership question, but its operation (a product, then a ratio split) runs through many caselets. These three are CLAT-style practice, not past questions.

🧪 CLAT-style practice (not a past question) CLAT-style: late joiners
Three college friends set up a thrift-clothing store. Nisha invested ₹80,000 at the start of the year. Dev joined 3 months later with ₹1,20,000. Farah joined 6 months after the start with ₹1,60,000. Nobody withdrew any money, and the profit at the end of the year was ₹2,10,000.

What is Farah's share of the profit?

A₹93,333
B₹75,600
C₹70,000
D₹67,200
Reveal answer + reasoning
Answer: D
Months: 12, 9 and 6. Products in thousands: 960, 1,080, 960. Divide by 120: 8 : 9 : 8, 25 parts of ₹8,400. Farah = 8 × 8,400 = ₹67,200. Time: about 50 seconds.
Why the others fail
  • A — Splits by capital alone (2 : 3 : 4), giving Farah 4/9.
  • B — ₹75,600 is Dev's share. Wrong partner.
  • C — Equal three-way split. Partnership is never equal by default.
🧪 CLAT-style practice (not a past question) CLAT-style: find the time
Nisha started a T-shirt printing business with ₹30,000 at the beginning of the year. Her brother Dev joined some months later with ₹40,000. The year's profit of ₹51,000 was divided ₹27,000 to Nisha and ₹24,000 to Dev, by capital and time.

How many months after the business started did Dev join?

A8 months
B4 months
C6 months
D1 month 10 days
Reveal answer + reasoning
Answer: B
Capitals 3 : 4; profits 27 : 24 = 9 : 8. Time ratio = 9/3 : 8/4 = 3 : 2. Nisha's 12 months is 3 parts, so Dev's money worked 8 months: he joined after 4 months. Time: about 45 seconds.
Why the others fail
  • A — 8 months is how long Dev's money stayed.
  • C — No correct step gives 6. Inverting the ratio gives Dev 18 months, impossible in a year: the sign you flipped it.
  • D — Uses the profit ratio as the time ratio (12 × 8/9 = 10⅔ months), forgetting Dev's larger capital.
🧪 CLAT-style practice (not a past question) CLAT-style: working partner
Kiran and Farah run a tiffin service. Kiran invested ₹2,00,000 and Farah ₹3,00,000, both for the whole year. Farah manages the kitchen and, by agreement, first receives 20% of the annual profit as a management fee; the rest is shared in the ratio of capital. The annual profit was ₹1,50,000.

How much more does Farah receive in total than Kiran?

A₹30,000
B₹24,000
C₹54,000
D₹60,000
Reveal answer + reasoning
Answer: C
Fee = 20% of 1,50,000 = ₹30,000. ₹1,20,000 splits 2 : 3: Kiran ₹48,000, Farah ₹72,000 + 30,000 = ₹1,02,000. Difference = ₹54,000. Time: about 40 seconds.
Why the others fail
  • A — Ignores the fee: all ₹1,50,000 split 2 : 3.
  • B — Removes the fee but never pays it to Farah.
  • D — Splits the full profit and adds the fee too, paying out ₹1,80,000.
💥 Myth vs fact
Myth vs fact: partnership
🙅 Myth
Whoever invests the most earns the most.
Tap to bust it →
✅ Fact
Only if the months match. Rohan's ₹1,50,000 for 6 months earned less than Zoya's ₹1,20,000 for 12.
🙅 Myth
'Joined after 4 months' means 4 months of investment.
Tap to bust it →
✅ Fact
It means 12 − 4 = 8 months in a one-year business.
🙅 Myth
Losses are split equally, whatever the capital.
Tap to bust it →
✅ Fact
Losses follow the same capital × time ratio as profits.

Can you split a partnership profit under exam pressure?

🎯 Quick quiz
Five quick partnership checks
0 / 5

Q1. Aarav and Meher invest ₹18,000 and ₹24,000 for the same period. Profit: ₹14,000. Meher's share?

Q2. Zoya invests ₹50,000 for 12 months; Kabir joins after 4 months with ₹75,000. The profit-sharing ratio?

Rohan and Meher invest ₹40,000 and ₹60,000 in a stall. Meher joined a few months after the stall opened. The year's profit is ₹30,000.

Q3. What is Rohan's share?

Q4. Kabir starts with ₹90,000 and withdraws ₹30,000 after 6 months. Aarav invests ₹80,000 all year. Profit: ₹62,000. Kabir's share?

Q5. Profits of A and B are 5 : 3. A's money stayed 10 months, B's 6. Ratio of their capitals?

🎯 Partnership in a nutshell
  • Profit splits in the ratio of capital × time.
  • Same time for all? Just the capitals.
  • Simplify capitals and months separately, then multiply.
  • Capital changes mid-way? One product per slab.
  • Fee first, then split the rest. Losses use the same ratio.
📎 Formula card
  • Profit ratio = C1T1 : C2T2 : C3T3.
  • A's share = Profit × C1T1 ÷ sum of products.
  • Time ratio = P1/C1 : P2/C2; capital ratio = P1/T1 : P2/T2.
  • Joined after k months → 12 − k; left after k months → k.
  • Withdrawal: C × months before + (C − W) × months after.
  • Working partner: fee first, remainder in the ratio.

Frequently asked questions

How is profit shared in a partnership?
Profit is shared in the ratio of each partner's capital multiplied by the time it stayed invested. ₹40,000 for 12 months and ₹60,000 for 8 months both give 4,80,000, so the profit splits 1 : 1. If all partners invest for the same period, the ratio is simply their capitals.
What is the difference between simple and compound partnership?
In a simple partnership everyone invests for the same period, so profit follows the capital ratio. In a compound partnership the periods differ or capital changes mid-way, so multiply each capital by its own months before comparing. Most exam questions are compound, because the dates are the test.
How do you calculate profit share when a partner joins late?
Subtract the joining month from the total period. In a one-year business, a partner who joins after 4 months has money working for 8 months, so use capital × 8. Form the ratio with the others' products and split the profit by the parts method.
How do you find time when the profit and capital ratios are given?
Divide the profit ratio by the capital ratio, term by term. Capitals 3 : 4 and profits 9 : 8 give time 9/3 : 8/4 = 3 : 2. If the first partner stayed 12 months, the second stayed 8, so joined after 4. Check which number the question wants.
Is a working partner's salary included in the profit split?
No. A salary or fee agreed for a working partner is paid out of the profit first. Only the remainder is divided in the capital × time ratio, and the working partner gets both. Splitting the full profit and then adding the salary pays out more than the business earned.

Keep going

← Previous topic
The Unitary Method
Find the value of one, then anything. Plus the fixed-charge trap
Next topic →
Problems on Ages: The Constant-Gap Trick
The constant-gap rule, the unit method and option tests for ages
📚
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

Dividing a Quantity in a Given Ratio
The last step of every partnership sum is the parts method.
Combining Ratios: A:B, B:C and Overall Ratios
Capital ratio × time ratio is a compound ratio in disguise.
Time and Work: the LCM Method
Rupee-months and man-days are the same idea: amount × duration.
Weighted Average
Months act as weights on each partner's capital.
Caselet DI: Turning a CLAT Quant Passage into a Table
Partnership caselets are three rows and three columns once tabled.

Every topic in Ratio & Proportion

  1. 1.Ratio Basics: Simplifying and Comparing Ratios
  2. 2.Dividing a Quantity in a Given Ratio
  3. 3.Combining Ratios: A:B, B:C and Overall Ratios
  4. 4.Proportion, Third and Mean Proportional
  5. 5.Direct and Inverse Proportion
  6. 6.The Unitary Method
  7. 7.Partnership: Sharing Profit by Capital × Time (you're here)
  8. 8.Problems on Ages: The Constant-Gap Trick

Ready to practise?

Free CLAT UG drills, sectional tests and full mocks in the real exam-screen format — timer, palette, instant scoring and solutions.

Practise Ratio & Proportion drills →