# Partnership

Partnership: A partnership is a formal agreement between two or more parties to manage and operate a business and share its profits (and losses).

**Share to**

## Introduction

**Simple Partnership:**As you mentioned, in a simple partnership, all partners contribute capital for the same period. Profits and losses are shared based on a predetermined ratio outlined in the partnership agreement.**Compound Partnership:**Here, partners contribute capital for different duration. The profit-sharing ratio considers both the amount of capital invested and the investment period. Partners who contribute capital for a longer period typically get a larger share of the profits.**Working Partner:**These partners actively participate in managing and running the business. They contribute capital and their expertise or labor. They receive a salary (optional) and share in the profits based on the partnership agreement.**Sleeping Partner:**These partners are silent investors. They contribute capital but don’t take part in the day-to-day operations. They share in the profits based on their investment but don’t receive a salary.

###### 01 (a) Shares Calculation for Two Partners:

If the capitals of two partners are represented as `C1`

and `C2`

for the same period, and the total profit is `P`

, then the shares of the partners in the profit can be calculated using the following formula:

Share of Partner 1: `(C1 / (C1 + C2)) * P`

Share of Partner 2: `(C2 / (C1 + C2)) * P`

###### (b) Shares Calculation for Three Partners:

If the capitals of three partners are represented as `C1`

, `C2`

, and `C3`

for the same period, and the total profit is `P`

, then the shares of the partners in the profit can be calculated using the following formulas:

Share of Partner 1: `(C1 / (C1 + C2 + C3)) * P`

Share of Partner 2: `(C2 / (C1 + C2 + C3)) * P`

Share of Partner 3: `(C3 / (C1 + C2 + C3)) * P`

###### 02 (a) The shares of the partners in the profits can be calculated using the formula:

Partner’s share = Partner’s capital × Time period / Total capital × Total time period × Total profit

For two partners with capitals C1 and C2 for periods t1 and t2 respectively, the shares would be:

Partner 1’s share = C1 × t1 / (C1 + C2) × (t1 + t2) × P

Partner 2’s share = C2 × t2 / (C1 + C2) × (t1 + t2) × P

###### (b) For three partners with capitals C1, C2, and C3 for periods t1, t2, and t3 respectively, the shares would be:

Partner 1’s share = C1 × t1 / (C1 + C2 + C3) × (t1 + t2 + t3) × P

Partner 2’s share = C2 × t2 / (C1 + C2 + C3) × (t1 + t2 + t3) × P

Partner 3’s share = C3 × t3 / (C1 + C2 + C3) × (t1 + t2 + t3) × P

## Partnership Problems

**Problem 1: A and B start a business by investing $5000 and $7000 respectively. After 4 months, C joins them with a capital of $6000. If the profit at the end of the year is $6600, then find C’s share of profit.**

**Solution 1:** First, let’s find the ratio of their investments multiplied by the time they invested:

- A’s investment = $5000 * 12 months = $60,000
- B’s investment = $7000 * 12 months = $84,000
- C’s investment = $6000 * 8 months (as he joined after 4 months) = $48,000

Now, to find the ratio of their investments:

- A : B : C = 60,000 : 84,000 : 48,000
- Simplify this ratio: 5 : 7 : 4

Now, find C’s share:

- C’s share = (C’s investment / Total investment) * Total profit
- C’s share = (4 / (5 + 7 + 4)) * 6600
- C’s share = (4 / 16) * 6600
- C’s share = 1650

So, C’s share of the profit is $1650.

**Problem 2: X, Y, and Z started a business by investing $8000, $10,000, and $12,000 respectively. After 4 months, X withdrew $2000, Y withdrew $3000, and Z invested an additional $2000. If the total profit at the end of the year is $15,000, find each person’s share.**

**Solution 2**: First, let’s find the ratio of their investments multiplied by the time they invested:

- X’s investment = $8000 * 4 months = $32,000
- Y’s investment = $10,000 * 4 months = $40,000
- Z’s investment = $12,000 * 4 months = $48,000

After the changes:

- X’s investment = ($8000 – $2000) * 8 months (as he withdrew after 4 months) = $48,000
- Y’s investment = ($10,000 – $3000) * 8 months = $56,000
- Z’s investment = ($12,000 + $2000) * 8 months = $112,000

Now, find the ratio of their investments:

- X : Y : Z = 48,000 : 56,000 : 112,000
- Simplify this ratio: 3 : 7 : 14

Now, find each person’s share:

- X’s share = (3 / (3 + 7 + 14)) * 15000 = 1/8 * 15000 = $1875
- Y’s share = (7 / (3 + 7 + 14)) * 15000 = 7/24 * 15000 = $4375
- Z’s share = (14 / (3 + 7 + 14)) * 15000 = 7/12 * 15000 = $8750

So,

- X’s share is $1875,
- Y’s share is $4375, and
- Z’s share is $8750.

**Problem 3: A, B, and C started a business by investing $8000, $10,000, and $12,000 respectively. After 3 months, A withdrew $2000, B withdrew $3000, and C invested an additional $2000. If the total profit at the end of the year is $20,000, find each person’s share.**

**Solution 3**: First, let’s find the ratio of their investments multiplied by the time they invested:

- A’s investment = $8000 * 3 months = $24,000
- B’s investment = $10,000 * 3 months = $30,000
- C’s investment = $12,000 * 3 months = $36,000

After the changes:

- A’s investment = ($8000 – $2000) * 9 months (as he withdrew after 3 months) = $54,000
- B’s investment = ($10,000 – $3000) * 9 months = $63,000
- C’s investment = ($12,000 + $2000) * 9 months = $126,000

Now, find the ratio of their investments:

- A : B : C = 54,000 : 63,000 : 126,000
- Simplify this ratio: 3 : 7 : 14

Now, find each person’s share:

- A’s share = (3 / (3 + 7 + 14)) * 20000 = 1/8 * 20000 = $2500
- B’s share = (7 / (3 + 7 + 14)) * 20000 = 7/24 * 20000 = $5833.33 (approx)
- C’s share = (14 / (3 + 7 + 14)) * 20000 = 7/12 * 20000 = $11666.66 (approx)

So,

- A’s share is $2500,
- B’s share is approximately $5833.33, and
- C’s share is approximately $11666.66.

**Problem 4: A and B started a business by investing $4000 and $6000 respectively. After 3 months, C joins them with a capital of $8000. At the end of the year, the total profit is $4500. Find C’s share of profit.**

**Solution 4:** First, let’s find the ratio of their investments multiplied by the time they invested:

- A’s investment = $4000 * 12 months = $48,000
- B’s investment = $6000 * 12 months = $72,000
- C’s investment = $8000 * 9 months (as he joined after 3 months) = $72,000

Now, find the ratio of their investments:

- A : B : C = 48,000 : 72,000 : 72,000
- Simplify this ratio: 2 : 3 : 3

Now, find C’s share:

- C’s share = (3 / (2 + 3 + 3)) * 4500 = 3/8 * 4500 = $1687.50

So, C’s share of the profit is $1687.50.

**Problem 5: X, Y, and Z started a business by investing $5000, $6000, and $7000 respectively. After 4 months, X withdrew $1000, Y withdrew $2000, and Z withdrew $3000. If the total profit at the end of the year is $9000, find each person’s share.**

**Solution 5:** First, let’s find the ratio of their investments multiplied by the time they invested:

- X’s investment = $5000 * 4 months = $20,000
- Y’s investment = $6000 * 4 months = $24,000
- Z’s investment = $7000 * 4 months = $28,000

After the changes:

- X’s investment = ($5000 – $1000) * 8 months (as he withdrew after 4 months) = $32,000
- Y’s investment = ($6000 – $2000) * 8 months = $32,000
- Z’s investment = ($7000 – $3000) * 8 months = $32,000

Now, find the ratio of their investments:

- X : Y : Z = 32,000 : 32,000 : 32,000
- Simplify this ratio: 1 : 1 : 1

Now, find each person’s share:

- X’s share = (1 / (1 + 1 + 1)) * 9000 = 1/3 * 9000 = $3000
- Y’s share = (1 / (1 + 1 + 1)) * 9000 = 1/3 * 9000 = $3000
- Z’s share = (1 / (1 + 1 + 1)) * 9000 = 1/3 * 9000 = $3000

So, X’s, Y’s, and Z’s share of the profit are all $3000.

## FAQ’s

A partnership is a legal agreement between two or more parties to co-own and operate a business. Partners share profits, losses, and management responsibilities as outlined in the partnership agreement.

**General Partnership:**The most common type. All partners share equally in profits, losses, and management. They also have unlimited liability, meaning they are personally responsible for the partnership’s debts.**Limited Liability Partnership (LLP):**Partners have limited liability for the debts and obligations of the partnership. Their personal assets are generally protected from creditors.**Limited Partnership:**There are two types of partners:- General partners: Manage the business and have unlimited liability.
- Limited partners: Contribute capital but have limited involvement and liability.

**Simplicity and Flexibility:**Easier and less expensive to form compared to corporations.**Shared Skills and Knowledge:**Partners bring different expertise to the table.**Profit Sharing:**Partners share in the business’s profits.

**Unlimited Liability (for General Partnerships):**Partners can be held personally responsible for debts.**Potential for Disagreements:**Disagreements can lead to conflicts.**Difficulty Raising Capital:**May be harder to raise large amounts of capital compared to corporations.

Profits are typically shared based on a predetermined ratio outlined in the partnership agreement. This ratio can consider factors like capital contribution, time invested, or expertise brought to the business.

## MCQ’s

**1. To start a partnership business, what should be the minimum number of partners?**

- A) 2
- B) 10
- C) 4
- D) 20

**Answer: A**

**2. What type of agreement is used to form a partnership business?**

- A) Written agreement
- B) Oral agreement
- C) Written or oral agreement
- D) None of them

**Answer: C**

**3. In partnership, partners liabilities are**

- A) Unlimited
- B) Limited to the capital of the business
- C) Limited
- D) Both A and C

**Answer: A**

**4. Is a partnership firm considered as a separate legal entity?**

- A) No
- B) Yes
- C) Partially Yes

**Answer: A**

**5. What happens when interest on drawings is charged to partner?**

- A) Credited to partner’s current a/c
- B) Not shown in current account
- C) Debited to partner’s capital a/c
- D) None of the above

**Answer: C**

**6. What is the responsibility of partners in a partnership organisation?**

- Unlimited
- No Liability
- Limited to the capital of business
- Limited

**Answer: 1. Unlimited**

**7. When does the direct debit to partner’s capital a/c entry made in accounts?**

- Interest on Drawings is charged.
- Investment is made
- Capital is withdrawn
- Drawings are made

**Answer-: 1. Interest on Drawings is charged**

**8. What percentage of the partners’ capital is charged interest on without a partnership deed?**

- 6 % Per annum
- 12 % Per annum
- 14 % Per annum
- No interest is levied

**Answer: 4 No interest is levied.**

**9. In the absence of a partnership agreement, how will the earnings be split among the partners?**

- Equal
- Depending on the capital invested.
- Unequal
- Depending on the work experience.

**Answer: 1 Equal**

**10. Which of the partnership firm’s accounts cannot record rent paid to partners?**

- Depreciation Account
- Expenses Account
- Profit & Loss Account
- Salary Account

**Answer: 3 Profit & Loss Account**

**11. What is a partner in profits only?**

- A person who gives some money to a business but doesn’t play a big role in running it.
- A person who has a stake in the partnership and is involved in the day-to-day running.
- An 18-year-old partner
- A partner who gets into an agreement to share only the profits of the partnership firm and not the losses.

**Answer: 4 A partner who gets into an agreement to share only the profits of the partnership firm and not the losses**