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).
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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