Partnership: Key Concepts and Questions for Competitive Exams

Partnership: Key Concepts, Formulas, and Practice Questions

In competitive exams, Partnership is a critical topic in Quantitative Aptitude, commonly asked in exams like SSC, Banking, and Railways. The concept of partnership mainly revolves around sharing of profits and losses among partners based on their investments or contributions.

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Key Concepts & Formulas:

1. Definition of Partnership:
   A partnership is an arrangement where two or more individuals come together to operate a business and share its profits and losses according to an agreed-upon ratio.
2. Basic Formula:
   In a partnership, profits and losses are divided among the partners based on the ratio of their investments. Formula for Share of Profit or Loss: $$\text{Partner’s Share} = \frac{\text{Partner’s Investment}}{\text{Total Investment}} \times \text{Total Profit or Loss}$$Partner’s Share=Total InvestmentPartner’s Investment​×Total Profit or Loss
3. Partnership Types:
   • Fixed Capital Partnership: Each partner invests a fixed sum of money, and the profit or loss is shared according to the agreed ratio.
   • Variable Capital Partnership: The capital of the partners varies over time.
4. Time-Based Investment:
   If partners invest money at different times, the share of profit or loss is calculated based on the product of the amount invested and the time of investment. The formula for this is: $$\text{Share of Partner} = \frac{P_1 \times T_1}{\text{Total of (P × T) for all partners}}$$Share of Partner=Total of (P × T) for all partnersP1​×T1​​ where $P_1$P1​ is the investment of the first partner, and $T_1$T1​ is the time for which the money is invested.
5. Additional Contributions:
   If a partner makes an additional investment during the year, their share of profit is calculated based on the time they invested at the new amount.
6. Withdrawal of Capital:
   If a partner withdraws part of their capital during the partnership period, their share of profit is calculated based on the time the withdrawn capital was in use.

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Examples of Common Partnership Questions:

1. A and B enter into a partnership with investments of ₹30,000 and ₹50,000 respectively. If the total profit at the end of the year is ₹40,000, how much will A receive?

2. A, B, and C started a business with investments of ₹50,000, ₹60,000, and ₹90,000 respectively. If the total profit at the end of the year is ₹30,000, how much will C receive?

3. A and B started a business. A invested ₹10,000 and B invested ₹15,000. After 6 months, A withdrew ₹5,000. What is the share of A in the profit of ₹12,000 at the end of the year?

4. A and B invested in a business for 12 months. A invested ₹30,000 and B invested ₹45,000. After 6 months, A withdrew ₹5,000. How much will A receive from a total profit of ₹18,000?

5. A and B start a business with capital contributions of ₹12,000 and ₹18,000, respectively. After 6 months, A contributes ₹6,000 more. If the profit at the end of the year is ₹24,000, how will the profit be divided?

6. A and B enter into a partnership with investments of ₹10,000 and ₹20,000. After 4 months, B increases his investment to ₹30,000. If the total profit at the end of the year is ₹18,000, how much will each partner receive?

7. A invests ₹5,000 in a business for 8 months, and B invests ₹10,000 for 6 months. If the total profit is ₹7,500, what is A’s share of the profit?

8. A and B invest in a business. A invests ₹10,000 for 9 months, and B invests ₹12,000 for 6 months. If the profit is ₹8,000, how much will A get?

9. In a partnership, A invested ₹25,000 for 8 months, and B invested ₹30,000 for 6 months. What is A’s share if the profit is ₹50,000?

10. A invests ₹20,000 in a business for 3 months and ₹40,000 for the next 6 months. What is A’s share of the profit of ₹60,000 after 9 months?

Answer

Answers to Partnership Practice Questions:

1. A and B enter into a partnership with investments of ₹30,000 and ₹50,000 respectively. If the total profit at the end of the year is ₹40,000, how much will A receive?

• Answer:
  Total investment = ₹30,000 + ₹50,000 = ₹80,000.
  A’s share of the profit = $\frac{30,000}{80,000} \times 40,000 = ₹15,000$80,00030,000​×40,000=₹15,000.

2. A, B, and C started a business with investments of ₹50,000, ₹60,000, and ₹90,000 respectively. If the total profit at the end of the year is ₹30,000, how much will C receive?

• Answer:
  Total investment = ₹50,000 + ₹60,000 + ₹90,000 = ₹2,00,000.
  C’s share of the profit = $\frac{90,000}{2,00,000} \times 30,000 = ₹13,500$2,00,00090,000​×30,000=₹13,500.

3. A and B started a business. A invested ₹10,000 and B invested ₹15,000. After 6 months, A withdrew ₹5,000. What is the share of A in the profit of ₹12,000 at the end of the year?

• Answer:
  A’s total investment = ₹10,000 for 6 months and ₹5,000 for the next 6 months.
  B’s total investment = ₹15,000 for 12 months.
  A’s share of the profit: $$\text{A’s share} = \frac{(10,000 \times 6) + (5,000 \times 6)}{(10,000 \times 12) + (15,000 \times 12)} \times 12,000 = \frac{60,000 + 30,000}{120,000 + 180,000} \times 12,000 = ₹4,000$$A’s share=(10,000×12)+(15,000×12)(10,000×6)+(5,000×6)​×12,000=120,000+180,00060,000+30,000​×12,000=₹4,000

4. A and B invested in a business for 12 months. A invested ₹30,000 and B invested ₹45,000. After 6 months, A withdrew ₹5,000. How much will A receive from a total profit of ₹18,000?

• Answer:
  A’s investment = ₹30,000 for 6 months, ₹25,000 for 6 months.
  B’s investment = ₹45,000 for 12 months.
  A’s share of the profit: $$\text{A’s share} = \frac{(30,000 \times 6) + (25,000 \times 6)}{(30,000 \times 12) + (45,000 \times 12)} \times 18,000 = ₹6,000$$A’s share=(30,000×12)+(45,000×12)(30,000×6)+(25,000×6)​×18,000=₹6,000

5. A and B start a business with capital contributions of ₹12,000 and ₹18,000, respectively. After 6 months, A contributes ₹6,000 more. If the profit at the end of the year is ₹24,000, how will the profit be divided?

• Answer:
  A’s total investment = ₹12,000 for 6 months and ₹18,000 for 6 months.
  B’s total investment = ₹18,000 for 12 months.
  A’s share of the profit: $$\text{A’s share} = \frac{(12,000 \times 6) + (18,000 \times 6)}{(12,000 \times 12) + (18,000 \times 12)} \times 24,000 = ₹12,000$$A’s share=(12,000×12)+(18,000×12)(12,000×6)+(18,000×6)​×24,000=₹12,000

6. A and B enter into a partnership with investments of ₹10,000 and ₹20,000. After 4 months, B increases his investment to ₹30,000. If the total profit at the end of the year is ₹18,000, how much will each partner receive?

Answer:
A’s total investment = ₹10,000 for 12 months.
B’s total investment = ₹20,000 for 4 months and ₹30,000 for 8 months.
A’s share of the profit: $$\text{A’s share} = \frac{10,000 \times 12}{(10,000 \times 12) + (20,000 \times 4 + 30,000 \times 8)} \times 18,000 = ₹6,000$$A’s share=(10,000×12)+(20,000×4+30,000×8)10,000×12​×18,000=₹6,000 B’s share = ₹12,000.