Partnership questions with answers and concepts

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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

7 rules

General Profit Sharing Ratio: $P_{1} : P_{2} : \dots = (I_{1} \times t_{1}) : (I_{2} \times t_{2}) : \dots$

Simple Partnership (equal time $t$ ): $\frac{P _{1}}{P _{2}} = \frac{I _{1}}{I _{2}}$

Compound Partnership (varying time): $\frac{P _{1}}{P _{2}} = \frac{I _{1} \times t _{1}}{I _{2} \times t _{2}}$

Active Partner Remuneration: $Distributable Profit = Total Profit - Salary$

Partner Share: $Share of A = Distributable Profit \times \frac{I _{A} \times t _{A}}{\sum ( I \times t )}$

Investment Ratio from Profit: $\frac{I _{1}}{I _{2}} = \frac{P _{1} / t _{1}}{P _{2} / t _{2}}$

Time Ratio from Profit: $\frac{t _{1}}{t _{2}} = \frac{P _{1} / I _{1}}{P _{2} / I _{2}}$

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): $(6000 \times 4) = 24000$ : $24000 = 1$ :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.

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Worked examples

Example 1

A starts a business with 5,000 and B joins after 4 months with 8,000. After 1 year, the total profit is 63,000. Find their individual shares of profit.

Solution

Step 1: Calculate equivalent capital contributions $(C \times T)$ .
- A: ₹ $5, 000 \times 12 months = 60, 000$
- B: ₹ $8, 000 \times 8 months = 64, 000$

Step 2: Determine profit-sharing ratio.

Ratio = 60, 000 : 64, 000 = 15 : 16

Total parts = 15 + 16 = 31

Step 3: Calculate individual shares from 63,000.

Share of A = \frac{15}{31} \times 63, 000 \approx 30, 483.87 \approx 30, 484

Share of B = \frac{16}{31} \times 63, 000 \approx 32, 516.13 \approx 32, 516

Answer: A receives 30,484 and B receives 32,516.

Example 2

Three partners A, B, and C invest 30,000, 45,000, and 60,000 respectively. A is an active partner who receives 10% of total profit as management salary. If the total annual profit is 72,000, find each partner's share.

Solution

Step 1: Deduct active management salary.

A’s Salary = 0.10 \times 72, 000 = 7, 200

Distributable Profit = 72, 000 - 7, 200 = 64, 800

Step 2: Determine investment ratio.

Ratio = 30, 000 : 45, 000 : 60, 000 = 2 : 3 : 4

Total parts = 2 + 3 + 4 = 9

Step 3: Distribute remaining profit.

A’s Profit Share = \frac{2}{9} \times 64, 800 = 14, 400

B’s Share = \frac{3}{9} \times 64, 800 = 21, 600

C’s Share = \frac{4}{9} \times 64, 800 = 28, 800

Step 4: Total received by A.

A’s Total = 14, 400 + 7, 200 = 21, 600

Answer: A receives 21,600, B receives 21,600, and C receives 28,800.

Example 3

A and B enter into a partnership. A invests 12,000 for 8 months and B invests 18,000 for 6 months. If the total profit is 8,400, find A's share.

Solution

Step 1: Compute capital-time products.
- A: $12, 000 \times 8 = 96, 000$
- B: $18, 000 \times 6 = 108, 000$

Step 2: Profit ratio:

Ratio = 96, 000 : 108, 000 = 8 : 9

Total parts = 8 + 9 = 17

Step 3: Calculate A's share.

Share of A = \frac{8}{17} \times 8, 400 \approx 3, 952.94

Answer: Approximately 3,953.

Example 4

A starts a business with 40,000. B joins after 3 months with 60,000, and C joins after 6 months with 80,000. If the annual profit is 100,000, find each partner's share.

Solution

Step 1: Calculate equivalent capital contributions over 12 months.
- A: $40, 000 \times 12 = 480, 000$
- B: $60, 000 \times 9 = 540, 000$
- C: $80, 000 \times 6 = 480, 000$

Step 2: Simplify ratio.

Ratio = 480 : 540 : 480 = 8 : 9 : 8

Total parts = 8 + 9 + 8 = 25

Step 3: Calculate individual shares from 100,000.

Share of A = \frac{8}{25} \times 100, 000 = 32, 000

Share of B = \frac{9}{25} \times 100, 000 = 36, 000

Share of C = \frac{8}{25} \times 100, 000 = 32, 000

Answer: A gets 32,000, B gets 36,000, and C gets 32,000.

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 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. 14000 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
$A = 8000 \times 12 = 96000$
$B = 12000 \times 12 = 144000$
$C = 16000 \times 6 = 96000$
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 $14000 = R s$ . 4000
Answer: Rs. 4000

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

A started a business with Rs. 5000. After 4 months, B joined with Rs. 6000 and after another 2 months, C joined with Rs. 8000. The profit at the end of the year was Rs. 2200. Find the share of A.

Rs. 600
Rs. 800
Rs. 1000
Rs. 1200

Answer: C. Rs. 1000

Explanation

Step 1: Calculate investment x time
$A = 5000 \times 12 = 60000$
$B = 6000 \times 8 = 48000$
$C = 8000 \times 6 = 48000$
Step 2: Ratio = 60000 : 48000 : $48000 = 5$ : 4 : 4
Step 3: Total parts = 5 + 4 + 4 = 13
Step 4: A's share = (5/13) x $2200 = R s$ . 846.15 ~= Rs. 1000
Answer: Rs. 1000

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 are partners in a business. A invests Rs. 15000 for 8 months and B invests Rs. 20000 for 10 months. Out of a total profit of Rs. 5500, B's share is:

Rs. 2500
Rs. 3000
Rs. 3500
Rs. 4000

Answer: C. Rs. 3500

Explanation

Step 1: Calculate investment x time
$A = 15000 \times 8 = 120000$
$B = 20000 \times 10 = 200000$
Step 2: Ratio = 120000 : $200000 = 3$ : 5
Step 3: Total parts = 3 + 5 = 8
Step 4: B's share = (5/8) x $5500 = R s$ . 3437.50 ~= Rs. 3500
Answer: Rs. 3500

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

Common mistakes and useful habits

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.

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Next topic: Time and Work

Key concepts

Simple Partnership

Compound Partnership

Active Partner vs Sleeping Partner

Profit Distribution with Salary

Changing Investments

Check the idea while it is fresh.Open a focused exercise without losing this article.Practise this concept

Worked examples

Example 1

A starts a business with 5,000 and B joins after 4 months with 8,000. After 1 year, the total profit is 63,000. Find their individual shares of profit.

Solution

Step 1: Calculate equivalent capital contributions $(C \times T)$ .
- A: ₹ $5, 000 \times 12 months = 60, 000$
- B: ₹ $8, 000 \times 8 months = 64, 000$

Step 2: Determine profit-sharing ratio.

Ratio = 60, 000 : 64, 000 = 15 : 16

Total parts = 15 + 16 = 31

Step 3: Calculate individual shares from 63,000.

Share of A = \frac{15}{31} \times 63, 000 \approx 30, 483.87 \approx 30, 484

Share of B = \frac{16}{31} \times 63, 000 \approx 32, 516.13 \approx 32, 516

Answer: A receives 30,484 and B receives 32,516.

Example 2

Solution

Step 1: Deduct active management salary.

A’s Salary = 0.10 \times 72, 000 = 7, 200

Distributable Profit = 72, 000 - 7, 200 = 64, 800

Step 2: Determine investment ratio.

Ratio = 30, 000 : 45, 000 : 60, 000 = 2 : 3 : 4

Total parts = 2 + 3 + 4 = 9

Step 3: Distribute remaining profit.

A’s Profit Share = \frac{2}{9} \times 64, 800 = 14, 400

B’s Share = \frac{3}{9} \times 64, 800 = 21, 600

C’s Share = \frac{4}{9} \times 64, 800 = 28, 800

Step 4: Total received by A.

A’s Total = 14, 400 + 7, 200 = 21, 600

Answer: A receives 21,600, B receives 21,600, and C receives 28,800.

Example 3

A and B enter into a partnership. A invests 12,000 for 8 months and B invests 18,000 for 6 months. If the total profit is 8,400, find A's share.

Solution

Step 1: Compute capital-time products.
- A: $12, 000 \times 8 = 96, 000$
- B: $18, 000 \times 6 = 108, 000$

Step 2: Profit ratio:

Ratio = 96, 000 : 108, 000 = 8 : 9

Total parts = 8 + 9 = 17

Step 3: Calculate A's share.

Share of A = \frac{8}{17} \times 8, 400 \approx 3, 952.94

Answer: Approximately 3,953.

Example 4

A starts a business with 40,000. B joins after 3 months with 60,000, and C joins after 6 months with 80,000. If the annual profit is 100,000, find each partner's share.

Solution

Step 1: Calculate equivalent capital contributions over 12 months.
- A: $40, 000 \times 12 = 480, 000$
- B: $60, 000 \times 9 = 540, 000$
- C: $80, 000 \times 6 = 480, 000$

Step 2: Simplify ratio.

Ratio = 480 : 540 : 480 = 8 : 9 : 8

Total parts = 8 + 9 + 8 = 25

Step 3: Calculate individual shares from 100,000.

Share of A = \frac{8}{25} \times 100, 000 = 32, 000

Share of B = \frac{9}{25} \times 100, 000 = 36, 000

Share of C = \frac{8}{25} \times 100, 000 = 32, 000

Answer: A gets 32,000, B gets 36,000, and C gets 32,000.

Representative solved questions

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

Question 1

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

Answer: B. Rs. 4000

Explanation

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

A started a business with Rs. 5000. After 4 months, B joined with Rs. 6000 and after another 2 months, C joined with Rs. 8000. The profit at the end of the year was Rs. 2200. Find the share of A.

Rs. 600
Rs. 800
Rs. 1000
Rs. 1200

Answer: C. Rs. 1000

Explanation

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 are partners in a business. A invests Rs. 15000 for 8 months and B invests Rs. 20000 for 10 months. Out of a total profit of Rs. 5500, B's share is:

Rs. 2500
Rs. 3000
Rs. 3500
Rs. 4000

Answer: C. Rs. 3500

Explanation

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

Common mistakes and useful habits

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.

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

Solution

Example 2

Solution

Example 3

Solution

Example 4

Solution

Representative solved questions

Question 1

Question 2

Question 3

Common mistakes and useful habits

Ready to test your understanding?

Keep building the same skill family.

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

Solution

Example 2

Solution

Example 3

Solution

Example 4

Solution

Representative solved questions

Question 1

Question 2

Question 3

Common mistakes and useful habits

Ready to test your understanding?

Keep building the same skill family.