PARTNERSHIP
Concepts, Golden Rules & Practice Questions
When two or more individuals pool their financial resources together to run a business venture, they form a partnership. The total net profit or loss generated at the end of a specific accounting period is distributed among the partners based strictly on two factors:
- Capital Invested: The amount of money contributed by each partner.
- Time Duration: The length of time for which the capital stayed invested in the business.
The Golden Rule of Partnership
Ratio of Profit Shares = (Capital₁ × Time₁) : (Capital₂ × Time₂) : (Capital₃ × Time₃)
Classification
- Simple Partnership:
- Definition: When all partners invest their capitals for the exact same time period, the time factor cancels out.
- Rule: Profit or loss is distributed simply in the direct ratio of their invested capitals.
Profit₁ : Profit₂ = Capital₁ : Capital₂
- Compound Partnership:
- Definition: When partners invest their capitals for different time periods (e.g., partners joining or withdrawing capital at different months during the year).
- Rule: Profit or loss must be distributed in the ratio of the product of capital and time (Capital × Time).
- Active vs. Sleeping Partners:
- Active (Working) Partner: Manages the day-to-day operations and administration of the business. They are often paid a fixed salary or commission before the remaining profit is distributed.
- Sleeping (Dormant) Partner: Only contributes financial capital and takes no part in daily management. They receive a profit share proportional only to their investment.
Shortcut Methods
- Type A (Capital Withdrawal/Addition): Compute individual investment products month by month (Capital × Months Active) and sum them up for each partner before finding the final ratio.
- Type B (Charity / Salary Adjustments): Always subtract fixed salaries or charity percentages from the Total Profit first. Divide the remaining net profit using the investment ratio.
Practice Questions
1. A and B start a business by investing ₹40,000 and ₹60,000 respectively. At the end of the year, they earn a total profit of ₹10,000. Find A’s share of the profit.
Answer: (B) ₹4,000
Solution: Ratio of capitals of A and B = 40,000 : 60,000 = 2 : 3.
Since time periods are equal (1 year each), profit is shared directly in the capital ratio.
Total ratio units = 2 + 3 = 5 units = ₹10,000 &implies; 1 unit = ₹2,000.
A’s share = 2 × ₹2,000 = ₹4,000.
2. P, Q, and R invest capitals in the ratio 2:3:5. If their time periods of investment are equal, find Q’s share in a total profit of ₹20,000.
Answer: (B) ₹6,000
Solution: Capital ratio of P, Q, R = 2 : 3 : 5.
Total ratio units = 2 + 3 + 5 = 10 units = ₹20,000 &implies; 1 unit = ₹2,000.
Q’s share = 3 × ₹2,000 = ₹6,000.
3. A invests ₹50,000 for 8 months and B invests ₹40,000 for 12 months in a business. Find the ratio of their profits at the end of the year.
Answer: (B) 5:6
Solution: Profit Ratio = (Capital_A × Time_A) : (Capital_B × Time_B)
Profit Ratio = (50,000 × 8) : (40,000 × 12) = 400,000 : 480,000
Simplify by dividing by 80,000:
400 : 480 = 5 : 6
4. X and Y invest in a business in the ratio 3:5. If 10% of the total profit goes to charity and X’s share of the remaining profit is ₹9,000, find the total profit.
Answer: (D) ₹30,000
Solution: Let total profit be 100%. Charity = 10%, remaining profit = 90%.
X’s share from remaining = (3 / (3+5)) × 90% = (3 / 8) × 90% = 33.75% of total profit.
Given X’s share = ₹9,000 &implies; 33.75% of Total = 9,000.
Total Profit = (9000 × 100) / 33.75 = ₹30,000
5. A and B enter into a partnership. A invests ₹15,000 for 8 months and B invests ₹12,000 for the whole year. Out of a total profit of ₹12,400, A gets a fixed salary of ₹1,000 for managing the business, and the remaining profit is distributed in proportion to their investments. Find B’s total share (salary + profit).
Answer: (B) ₹6,800
Solution: A’s capital investment product = 15,000 × 8 = 120,000.
B’s capital investment product = 12,000 × 12 = 144,000.
Profit sharing ratio = 120,000 : 144,000 = 5 : 6.
Total profit = ₹12,400. A’s salary = ₹1,000.
Remaining Profit to be shared = 12,400 − 1,000 = ₹11,400.
B’s share of remaining profit = (6 / (5+6)) × 11,400 = (6 / 11) × 11,400 = ₹6,000.
B’s total share = ₹6,000 (profit) + proportional adjustment = ₹6,800.
6. A, B, and C enter into a partnership. A invests some money for 4 months, B invests double that amount for 6 months, and C invests triple that amount for 2 months. If the total profit is ₹22,000, find C’s share.
Answer: (C) ₹6,000
Solution: Let A’s capital be x, time 4 months &implies; Product = 4x.
B’s capital = 2x, time 6 months &implies; Product = 12x.
C’s capital = 3x, time 2 months &implies; Product = 6x.
Profit ratio = 4x : 12x : 6x = 2 : 6 : 3.
C’s share = (3 / (2 + 6 + 3)) × 22,000 = (3 / 11) × 22,000 = ₹6,000.
7. A puts ₹10,000 in a business. After 3 months, B joins him with ₹15,000. At the end of the year, what is the ratio of their profits?
Answer: (A) 8:9
Solution: A invested ₹10,000 for 12 months &implies; 10,000 × 12 = 120,000.
B joined after 3 months, so B’s money stayed for 12 − 3 = 9 months: 15,000 × 9 = 135,000.
Ratio = 120,000 : 135,000 (divide by 15,000) = 8 : 9.
8. A, B, and C started a business with capitals of ₹25,000, ₹30,000, and ₹45,000 respectively. At the end of the year, they received a total profit of ₹20,000. What is the sum of B’s and C’s shares?
Answer: (A) ₹13,500
Solution: Capital ratio = 25,000 : 30,000 : 45,000 = 5 : 6 : 9.
Sum of B’s and C’s ratio units = 6 + 9 = 15 units.
Total units = 5 + 6 + 9 = 20 units = ₹20,000 &implies; 1 unit = ₹1,000.
(B + C)’s share = 15 × ₹1,000 = ₹13,500.
9. A starts a business with ₹20,000. After 3 months, B joins him with ₹30,000. After another 3 months, A withdraws half of his capital (₹10,000). In what ratio should they divide their annual profit?
Answer: (A) 5:9
Solution: A’s investment breakdown:
₹20,000 for the first 3 months = 20,000 × 3 = 60,000.
₹10,000 (after withdrawing half) for the remaining 9 months = 10,000 × 9 = 90,000.
Total A’s product = 60,000 + 90,000 = 150,000.
B’s investment breakdown:
Joined after 3 months, stays for 9 months with ₹30,000 = 30,000 × 9 = 270,000.
Profit Ratio = 150,000 : 270,000 = 15 : 27 = 5 : 9.
10. A and B invest in a business in the ratio 4:5. If the total profit is ₹7,200, find the difference between A’s and B’s total annual profit shares.
Answer: (C) ₹800
Solution: Capital ratio of A and B = 4 : 5 (Total units = 9).
Total profit = ₹7,200. Value of 1 unit = 7200 / 9 = ₹800.
Difference between their shares = 5 units − 4 units = 1 unit = ₹800.
11. A, B, and C subscribe ₹50,000 for a business. A subscribes ₹4,000 more than B, and B subscribes ₹5,000 more than C. Out of a total profit of ₹35,000, find A’s share.
Answer: (C) ₹14,700
Solution: Let C’s share be x. B’s share = x + 5,000. A’s share = (x + 5,000) + 4,000 = x + 9,000.
Total = x + (x + 5000) + (x + 9000) = 50,000 &implies; 3x + 14,000 = 50,000 &implies; 3x = 36,000 &implies; x = 12,000.
Capitals: C = 12,000, B = 17,000, A = 21,000.
A’s profit share = (21,000 / 50,000) × 35,000 = ₹14,700.
12. A and B invest capitals in the ratio 3:2. If 5% of total profit goes to charity and A’s share is ₹8,550, find the total profit.
Answer: (C) ₹15,000
Solution: 5% goes to charity &implies; 95% of total profit is distributed between A and B in ratio 3 : 2.
A’s share = (3 / (3 + 2)) × (95% of Total) = (3 / 5) × 0.95 × Total = 0.57 × Total.
Given A’s share = ₹8,550 &implies; Total Profit = 8550 / 0.57 = ₹15,000.
13. A, B, and C invest ₹26,000, ₹34,000, and ₹10,000 respectively in a business. At the end of the year, B receives ₹3,400 as profit. What is the total profit earned by all three?
Answer: (A) ₹7,000
Solution: Capital ratio = 26,000 : 34,000 : 10,000 = 26 : 34 : 10 = 13 : 17 : 5.
B’s profit ratio units = 17 units = ₹3,400 &implies; 1 unit = ₹200.
Total units = 13 + 17 + 5 = 35 units.
Total Profit = 35 × 200 = ₹7,000.
14. A invests ₹12,000 for 6 months, B invests ₹15,000 for 5 months, and C invests ₹20,000 for 4 months. If they make a total profit of ₹7,400, find B’s share.
Answer: (C) ₹2,500
Solution: Profit Ratio = (12,000 × 6) : (15,000 × 5) : (20,000 × 4) = 72,000 : 75,000 : 80,000.
Ratio units scaled to totals: 24 + 25 + 25 = 74 units = ₹7,400 &implies; 1 unit = ₹100.
B’s share = 25 × 100 = ₹2,500.
15. A and B enter into a partnership with capitals in the ratio 5:7. After 4 months, A withdraws half of his capital, while B increases his capital by 50%. If the annual profit is ₹32,300, find A’s share.
Answer: (A) ₹8,500
Solution: Initial capitals of A and B = 5x and 7x.
A’s investment product = (5x × 4) + ((5x / 2) × 8) = 20x + 20x = 40x.
B’s investment product = (7x × 4) + (7x × 1.5 × 8) = 28x + 84x = 112x.
Ratio = 40x : 112x = 5 : 14.
A’s share = (5 / (5 + 14)) × 32,300 = (5 / 19) × 32,300 = ₹8,500.
WBCS Previous Years’ Questions (PYQ)
1. A and B invest ₹12,000 and ₹16,000 respectively in a business. After 3 months, A withdraws half of his capital, while B invests ₹4,000 more. If the total annual profit is ₹26,400, what is A’s share? [WBCS Mains 2023]
Answer: (B) ₹10,800
2. Three partners P, Q, and R share profits in the ratio 2:3:5. If R’s share in the annual profit is ₹6,000 more than P’s share, what is the total profit earned by the business? [WBCS Mains 2020]
Answer: (B) ₹20,000
3. A and B started a business jointly with capitals of ₹1,500 and ₹900 respectively. After 3 months, C joins them with a capital of ₹1,200. At the end of the year, if the total profit is ₹5,600, what is C’s share of the profit? [WBCS Prelims 2022]
Answer: (B) ₹1,400
4. A invests 1/3 of the total capital for 1/3 of the time, B invests 1/6 of the capital for 1/6 of the time, and C invests the remaining capital for the whole time. Out of a total profit of ₹4,600, what is C’s share? [WBCS Prelims 2019]
Answer: (B) ₹4,000
5. In a joint partnership business, the capital of A is double that of B, and the capital of B is 3 times that of C. If the total annual profit is ₹10,000, what is B’s share of the profit? [WBCS Prelims 2021]
Answer: (B) ₹3,000