Partnership

Profit sharing in business

Partnership deals with profit distribution among business partners based on their investment contributions and duration. It involves simple partnerships (equal time periods) and compound partnerships (different time periods), including concepts of sleeping and active partners who contribute differently to the business.

Key Formulas

\text{Profit Ratio = (Investment x Time) for each partner}

\text{Simple Partnership: Profit shared in ratio of investments when time is same}

\text{Compound Partnership: Profit shared in ratio of (Investment x Time)}

\text{Active Partner gets extra salary/remuneration before profit sharing}

\text{Sleeping Partner only invests, doesn't work; Active Partner manages business}

\text{After paying active partner's salary, remaining profit shared by investment ratio}

\text{If investments are A:B and times are t :t , profit ratio = (Axt ):(Bxt )}

Key Concepts

Simple Partnership

In a simple partnership, all partners invest for the same duration of time. The profit or loss is distributed in the ratio of their investments. For example, if A invests 5000 and B invests 3000 for the same period, profit is shared in 5:3 ratio. No time factor is considered since all partners invest for equal durations.

Compound Partnership

In a compound partnership, partners invest for different time periods. Profit is distributed in the ratio of the product of investment and time (Investment x Time). For example, if A invests 4000 for 6 months and B invests 6000 for 4 months, profit ratio = (4000x6):(6000x4) = 24000:24000 = 1:1. This ensures fair distribution accounting for both capital and duration.

Active Partner vs Sleeping Partner

An active partner manages the business operations, devotes time and effort, and often receives a salary or remuneration before profit distribution. A sleeping partner (or dormant partner) only contributes capital without participating in management. The active partner's salary is deducted from total profit first, then remaining profit is distributed based on investment ratios.

Profit Distribution with Salary

When an active partner receives a fixed salary: (1) Calculate gross profit, (2) Deduct active partner's salary to get net profit, (3) Distribute net profit among all partners in their investment ratio, (4) Active partner's total share = Salary + Profit share. This recognizes both capital contribution and managerial effort.

Changing Investments

When partners change their investments during the partnership period, calculate equivalent capital for one month (or one year). For example, if A invests 5000 for 4 months then 8000 for 8 months, equivalent capital = (5000x4) + (8000x8) = 20000 + 64000 = 84000. Compare these equivalent capitals to find profit ratio.

Solved Examples

Problem 1:

A starts a business with 5000 and B joins after 4 months with 8000. After 1 year, the profit is 63000. Find their shares.

Solution:

Step 1: Calculate investment periods.
A invests for 12 months, B invests for 8 months (joined after 4 months).

Step 2: Calculate equivalent capitals.
A: 5000 x 12 = 60000
B: 8000 x 8 = 64000

Step 3: Find profit ratio.
Ratio = 60000:64000 = 15:16

Step 4: Calculate individual shares.
Total parts = 15 + 16 = 31
A's share = (15/31) x 63000 = 30483.87 ~= 30484
B's share = (16/31) x 63000 = 32516.13 ~= 32516

Problem 2:

Three partners A, B, C invest 30000, 45000, 60000 respectively. A is an active partner who receives 10% of profit as salary. If total profit is 72000, find each partner's share.

Solution:

Step 1: Calculate A's salary.
Salary = 10% of 72000 = 7200

Step 2: Calculate net profit for distribution.
Net profit = 72000 - 7200 = 64800

Step 3: Find investment ratio.
A:B:C = 30000:45000:60000 = 2:3:4

Step 4: Distribute net profit.
Total parts = 2 + 3 + 4 = 9
A's profit share = (2/9) x 64800 = 14400
B's share = (3/9) x 64800 = 21600
C's share = (4/9) x 64800 = 28800

Step 5: Calculate A's total.
A's total = Salary + Profit share = 7200 + 14400 = 21600

Problem 3:

A and B enter partnership. A invests 12000 for 8 months and B invests 18000 for 6 months. If total profit is 8400, find A's share.

Solution:

Step 1: Calculate equivalent capitals.
A: 12000 x 8 = 96000
B: 18000 x 6 = 108000

Step 2: Find profit ratio.
Ratio = 96000:108000 = 8:9

Step 3: Calculate total parts.
Total parts = 8 + 9 = 17

Step 4: Find A's share.
A's share = (8/17) x 8400 = 3952.94 ~= 3953

Problem 4:

A starts with 40000, B joins after 3 months with 60000, and C joins after 6 months with 80000. Annual profit is 100000. Find each share.

Solution:

Step 1: Calculate investment periods.
A: 12 months, B: 9 months, C: 6 months

Step 2: Calculate equivalent capitals.
A: 40000 x 12 = 480000
B: 60000 x 9 = 540000
C: 80000 x 6 = 480000

Step 3: Find profit ratio.
Ratio = 480000:540000:480000 = 48:54:48 = 8:9:8

Step 4: Calculate shares.
Total parts = 8 + 9 + 8 = 25
A's share = (8/25) x 100000 = 32000
B's share = (9/25) x 100000 = 36000
C's share = (8/25) x 100000 = 32000

Tips & Tricks

Always convert time periods to the same unit (months or years) before calculating equivalent capital.
When a partner joins mid-way, subtract the joining delay from total period to get their investment duration.
For changing investments, calculate weighted average capital: (Investment x Duration for each period).
Active partner's salary is deducted BEFORE profit distribution, not after.
If profit ratio is given and you need to find investment/time, use inverse ratios with appropriate adjustments.
Check if the problem mentions active/sleeping partners - this indicates salary considerations.

Ready to practice?

Test your understanding with questions and get instant feedback.

Start Exercise →