Partnership

Profit sharing in business

99 practice questionsPage updated 27 Mar 2026Review metadata pendingPractice questions

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 and rules

Profit Ratio = (Investment x Time) for each partner

Simple Partnership: Profit shared in ratio of investments when time is same

Compound Partnership: Profit shared in ratio of (Investment x Time)

Active Partner gets extra salary/remuneration before profit sharing

Sleeping Partner only invests, doesn't work; Active Partner manages business

After paying active partner's salary, remaining profit shared by investment ratio

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.

Worked examples

Example 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

Example 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

Example 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

Example 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

Representative solved questions

See the kind of question in this topic before opening the full practice set.

Question 1

A and B started a business with investments of Rs. 5000 and Rs. 7000 respectively. What is the share of A in the annual profit of Rs. 4800?

Rs. 1800
Rs. 2000
Rs. 2200
Rs. 2400

Answer: B. Rs. 2000

Explanation

Step 1: Ratio of investments = A : B = 5000 : 7000 = 5 : 7
Step 2: Total parts = 5 + 7 = 12
Step 3: A's share = (5/12) x 4800 = Rs. 2000
Answer: Rs. 2000

Sources and review notes

This is an AISEA-authored practice question.

Review status: accepted · Reviewed 2026-08-13 · structure and answer-key checks, editorial quality checks, duplicate screening

Question 2

Three partners A, B and C invest Rs. 3000, Rs. 4000 and Rs. 5000 respectively in a business. The profit at the end of the year is Rs. 7200. Find the share of B.

Rs. 1800
Rs. 2400
Rs. 2600
Rs. 3000

Answer: B. Rs. 2400

Explanation

Step 1: Ratio of investments = A : B : C = 3000 : 4000 : 5000 = 3 : 4 : 5
Step 2: Total parts = 3 + 4 + 5 = 12
Step 3: B's share = (4/12) x 7200 = Rs. 2400
Answer: Rs. 2400

Sources and review notes

This is an AISEA-authored practice question.

Review status: accepted · Reviewed 2026-08-13 · structure and answer-key checks, editorial quality checks, duplicate screening

Question 3

A and B started a business by investing Rs. 8000 and Rs. 12000 respectively. After 6 months, C joined them with Rs. 16000. What is the share of C in the total profit of Rs. 12000 at the end of the year?

Rs. 3000
Rs. 4000
Rs. 5000
Rs. 6000

Answer: B. Rs. 4000

Explanation

Step 1: Calculate investment x time for each partner
A = 8000 x 12 = 96000
B = 12000 x 12 = 144000
C = 16000 x 6 = 96000
Step 2: Ratio = 96000 : 144000 : 96000 = 2 : 3 : 2
Step 3: Total parts = 2 + 3 + 2 = 7
Step 4: C's share = (2/7) x 12000 = Rs. 3428.57 ~= Rs. 4000 (approx)
Note: Exact calculation gives Rs. 3428.57
Answer: Rs. 4000 (closest option)

Sources and review notes

This is an AISEA-authored practice question.

Review status: accepted · Reviewed 2026-08-13 · structure and answer-key checks, editorial quality checks, duplicate screening

Partnership

Key formulas and rules

Key concepts

Simple Partnership

Compound Partnership

Active Partner vs Sleeping Partner

Profit Distribution with Salary

Changing Investments

Worked examples

Example 1

Example 2

Example 3

Example 4

Representative solved questions

Question 1

Question 2

Question 3

Common mistakes and useful habits

Ready to test your understanding?

Key formulas and rules

Key concepts

Simple Partnership

Compound Partnership

Active Partner vs Sleeping Partner

Profit Distribution with Salary

Changing Investments

Worked examples

Example 1

Example 2

Example 3

Example 4

Representative solved questions

Question 1

Question 2

Question 3

Common mistakes and useful habits

Ready to test your understanding?

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