Partnership

Scenario

Two college friends build a SaaS side-hustle. One invests Rs50,000 for 12 months, the other joins later with Rs1,00,000 for 6 months. Who deserves a bigger cut of the ARR?

Mental model

Profit share is strictly the area under the investment-time curve.

Your reward is proportional to how much money you put in, multiplied by how long it was actively working for the business.

Formula

Profit(A) : Profit(B) = (Capital(A) x Time(A)) : (Capital(B) x Time(B)). For 3+ partners: Profit ratio = (C1 x T1) : (C2 x T2) : (C3 x T3). Working partner allowance: subtract the working partner's salary from total profit FIRST, then split the remainder by capital-time ratio.

Calculate Capital x Time for each partner, then simplify to the lowest ratio. Use that ratio as parts to divide the total profit. If a partner invests at different amounts at different periods, compute C x T for each period and sum them.

Pattern discovery

See how profit ratio changes with capital and time.

• A: 10k for 12m, B: 20k for 6m -> Capital-time: 120k vs 120k -> Profit 1:1
• A: 10k for 6m, B: 10k for 12m -> Capital-time: 60k vs 120k -> Profit 1:2

What single number captures both the size and duration of each investment?

Rule: Profit ratio is exactly the ratio of the products of (Capital x Time). More capital OR more time gives a proportionally larger share.

Worked example

Problem: P starts a business with Rs30,000. After 4 months, Q joins with Rs45,000. After another 2 months, R joins with Rs60,000. They work till year-end. If the annual profit is Rs88,000, find each partner's share.

1. Calculate capital-time for each: P = 30000 x 12 = 360000. Q joins at month 4, so works for 8 months: 45000 x 8 = 360000. R joins at month 6, so works for 6 months: 60000 x 6 = 360000.
2. Profit ratio = 360000 : 360000 : 360000 = 1 : 1 : 1.
3. Total profit = Rs88,000. Each partner gets 88000 / 3 = Rs29,333.33.
4. Sanity-check: All three products are equal (360k), so 3 equal shares. Total = 3 x 29333 = 88000. Correct.

Answer: Each partner gets Rs29,333.33.

Shortcuts

• Working Partner Allowance: Subtract the working partner's fixed salary/percentage from total profit BEFORE splitting by capital ratio. (Profit = 100. A gets 10% for managing. Split remaining 90 by capital-time ratio.)

Common mistakes

• Ignoring the time factor: Do not divide profits just by the capital invested. A late investor's capital must be multiplied by fewer months than an early investor.

Glossary

proportional

When one amount changes directly based on the size of another amount.

capital

The total amount of money used to start or run a business.

simplify

To reduce numbers in a ratio or fraction to their smallest possible whole numbers.

Recall questions

• A invests 20k for 12 months, B invests 40k for 6 months. What is their profit ratio?
• If profit ratio is 2:3 and time ratio is 1:2, what is the capital ratio?
• A, B, C rent a pasture. A puts 10 cows for 7 months, B puts 12 cows for 5 months, C puts 15 cows for 3 months. What is the ratio of rent?

Questions & answers

A starts a business with Rs40,000. After 3 months, B joins with Rs60,000. If the total profit at year-end is Rs34,000, what is A's share?

Rs16,000

Approach: A: 40k x 12 = 480. B: 60k x 9 = 540. Ratio = 480:540 = 8:9. Total = 17 parts = 34k. 1 part = 2k. A's share = 8 x 2k = 16,000.

A, B, and C invest in a business. A invests 1/3 of total capital, B invests 1/4, and C the rest. If profit is Rs24,000, what is C's share?

Rs10,000

Approach: C's capital = 1 - (1/3 + 1/4) = 1 - 7/12 = 5/12. Since time is same for all, profit ratio = 1/3 : 1/4 : 5/12 = 4:3:5. Total 12 parts = 24k. C's share = 5 x 2k = 10,000.

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