Master the concepts of partnerships with our comprehensive guide. Learn about profit sharing, capital investment, and complex problem-solving techniques.
Understanding the basic concepts of partnerships and their properties.
Key Terms:
Important Points:
Example 1: Basic Partnership
Q1.
A and B invest ₹10,000 and ₹15,000 respectively in a business. Find their profit sharing ratio.
Solution:
Profit sharing ratio = 10000:15000 = 2:3
Q2.
A, B, and C invest ₹20,000, ₹30,000, and ₹50,000 respectively. Find their profit sharing ratio.
Solution:
Profit sharing ratio = 20000:30000:50000 = 2:3:5
Q3.
A and B invest ₹25,000 and ₹35,000 respectively. If the total profit is ₹12,000, find their individual shares.
Solution:
Profit sharing ratio = 25000:35000 = 5:7
A's share = (5/12) × 12000 = ₹5,000
B's share = (7/12) × 12000 = ₹7,000
Q4.
A, B, and C invest ₹15,000, ₹25,000, and ₹35,000 respectively. If the total profit is ₹30,000, find their individual shares.
Solution:
Profit sharing ratio = 15000:25000:35000 = 3:5:7
A's share = (3/15) × 30000 = ₹6,000
B's share = (5/15) × 30000 = ₹10,000
C's share = (7/15) × 30000 = ₹14,000
Solving problems involving simple partnerships.
Formulas:
Example 2: Simple Partnership
Q1. A and B invest ₹20,000 and ₹30,000 for 1 year. If the total profit is ₹25,000, find their shares.
Solution:
Profit sharing ratio = 20000:30000 = 2:3
A's share = (2/5) × 25000 = ₹10,000
B's share = (3/5) × 25000 = ₹15,000
Q2. A, B, and C invest ₹15,000, ₹25,000, and ₹35,000 for 1 year. If the total profit is ₹30,000, find their shares.
Solution:
Profit sharing ratio = 15000:25000:35000 = 3:5:7
A's share = (3/15) × 30000 = ₹6,000
B's share = (5/15) × 30000 = ₹10,000
C's share = (7/15) × 30000 = ₹14,000
Q3. A and B invest ₹25,000 and ₹35,000 for 1 year. If A's share of profit is ₹10,000, find the total profit.
Solution:
Profit sharing ratio = 25000:35000 = 5:7
Let total profit be x
(5/12) × x = 10000
x = ₹24,000
Q4. A, B, and C invest ₹20,000, ₹30,000, and ₹40,000 for 1 year. If B's share of profit is ₹15,000, find the total profit.
Solution:
Profit sharing ratio = 20000:30000:40000 = 2:3:4
Let total profit be x
(3/9) × x = 15000
x = ₹45,000
Solving problems involving compound partnerships.
Formulas:
Example 2: Compound Partnership
Q1.
A invests ₹20,000 for 6 months and B invests ₹30,000 for 4 months. Find their profit sharing ratio.
Solution:
A's investment = 20000 × 6 = ₹1,20,000
B's investment = 30000 × 4 = ₹1,20,000
Profit sharing ratio = 1:1
Q2.
A invests ₹25,000 for 8 months, B invests ₹30,000 for 6 months, and C invests ₹40,000 for 4 months. Find their profit sharing ratio.
Solution:
A's investment = 25000 × 8 = ₹2,00,000
B's investment = 30000 × 6 = ₹1,80,000
C's investment = 40000 × 4 = ₹1,60,000
Profit sharing ratio = 200:180:160 = 10:9:8
Q3.
A and B invest ₹15,000 and ₹25,000 respectively. A withdraws after 4 months while B stays for the whole year. If the total profit is ₹18,000, find their shares.
Solution:
A's investment = 15000 × 4 = ₹60,000
B's investment = 25000 × 12 = ₹3,00,000
Profit sharing ratio = 60:300 = 1:5
A's share = (1/6) × 18000 = ₹3,000
B's share = (5/6) × 18000 = ₹15,000
Q4.
A, B, and C invest ₹20,000, ₹30,000, and ₹40,000 respectively. A stays for 6 months, B for 8 months, and C for the whole year. If the total profit is ₹24,000, find their shares.
Solution:
A's investment = 20000 × 6 = ₹1,20,000
B's investment = 30000 × 8 = ₹2,40,000
C's investment = 40000 × 12 = ₹4,80,000
Profit sharing ratio = 120:240:480 = 1:2:4
A's share = (1/7) × 24000 = ₹3,428.57
B's share = (2/7) × 24000 = ₹6,857.14
C's share = (4/7) × 24000 = ₹13,714.29
Solving problems involving working partners.
Formulas:
Example 3: Working Partner
Q1.
A invests ₹50,000 and works for the business, while B invests ₹1,00,000 as a sleeping partner. If the total profit is ₹30,000, find their shares.
Solution:
First, calculate capital ratio: 50000:100000 = 1:2
Let A's salary be x
Remaining profit = 30000 - x
A's share = x + (1/3)(30000 - x)
B's share = (2/3)(30000 - x)
Q2.
A invests ₹40,000 and works for the business, while B and C invest ₹60,000 each as sleeping partners. If the total profit is ₹45,000 and A's salary is ₹5,000, find their shares.
Solution:
Capital ratio = 40000:60000:60000 = 2:3:3
Remaining profit = 45000 - 5000 = ₹40,000
A's share = 5000 + (2/8)(40000) = ₹15,000
B's share = (3/8)(40000) = ₹15,000
C's share = (3/8)(40000) = ₹15,000
Q3.
A invests ₹30,000 and works for the business, while B invests ₹70,000 as a sleeping partner. If A's salary is ₹4,000 and the total profit is ₹20,000, find their shares.
Solution:
Capital ratio = 30000:70000 = 3:7
Remaining profit = 20000 - 4000 = ₹16,000
A's share = 4000 + (3/10)(16000) = ₹8,800
B's share = (7/10)(16000) = ₹11,200
Q4.
A and B invest ₹25,000 each and both work for the business, while C invests ₹50,000 as a sleeping partner. If each working partner gets ₹3,000 as salary and the total profit is ₹25,000, find their shares.
Solution:
Capital ratio = 25000:25000:50000 = 1:1:2
Total salary = 3000 × 2 = ₹6,000
Remaining profit = 25000 - 6000 = ₹19,000
A's share = 3000 + (1/4)(19000) = ₹7,750
B's share = 3000 + (1/4)(19000) = ₹7,750
C's share = (2/4)(19000) = ₹9,500
Solving problems involving sleeping partners.
Formulas:
Example 4: Sleeping Partner
Q1.
A invests ₹40,000 and works for the business, while B invests ₹60,000 as a sleeping partner. If the total profit is ₹25,000, find their shares.
Solution:
Capital ratio = 40000:60000 = 2:3
Let A's salary be x
Remaining profit = 25000 - x
A's share = x + (2/5)(25000 - x)
B's share = (3/5)(25000 - x)
Q2.
A invests ₹30,000 and works for the business, while B and C invest ₹45,000 each as sleeping partners. If the total profit is ₹30,000 and A's salary is ₹4,000, find their shares.
Solution:
Capital ratio = 30000:45000:45000 = 2:3:3
Remaining profit = 30000 - 4000 = ₹26,000
A's share = 4000 + (2/8)(26000) = ₹10,500
B's share = (3/8)(26000) = ₹9,750
C's share = (3/8)(26000) = ₹9,750
Q3.
A invests ₹35,000 and works for the business, while B invests ₹65,000 as a sleeping partner. If A's salary is ₹5,000 and the total profit is ₹20,000, find their shares.
Solution:
Capital ratio = 35000:65000 = 7:13
Remaining profit = 20000 - 5000 = ₹15,000
A's share = 5000 + (7/20)(15000) = ₹10,250
B's share = (13/20)(15000) = ₹9,750
Q4.
A and B invest ₹20,000 each and both work for the business, while C invests ₹60,000 as a sleeping partner. If each working partner gets ₹2,500 as salary and the total profit is ₹22,000, find their shares.
Solution:
Capital ratio = 20000:20000:60000 = 1:1:3
Total salary = 2500 × 2 = ₹5,000
Remaining profit = 22000 - 5000 = ₹17,000
A's share = 2500 + (1/5)(17000) = ₹5,900
B's share = 2500 + (1/5)(17000) = ₹5,900
C's share = (3/5)(17000) = ₹10,200
Key Theorems:
Example 5: Advanced Concepts
Q1.
A and B start a business with ₹30,000 and ₹40,000 respectively. After 6 months, A withdraws half his capital and B adds ₹20,000 more. If the total profit is ₹25,000, find their shares.
Solution:
A's investment = 30000 × 6 + 15000 × 6 = ₹2,70,000
B's investment = 40000 × 6 + 60000 × 6 = ₹6,00,000
Profit sharing ratio = 270:600 = 9:20
A's share = (9/29) × 25000 = ₹7,758.62
B's share = (20/29) × 25000 = ₹17,241.38
Q2.
A, B, and C start a business with ₹25,000, ₹35,000, and ₹45,000 respectively. After 4 months, A adds ₹5,000, B withdraws ₹10,000, and C adds ₹15,000. If the total profit is ₹30,000, find their shares.
Solution:
A's investment = 25000 × 4 + 30000 × 8 = ₹3,40,000
B's investment = 35000 × 4 + 25000 × 8 = ₹3,40,000
C's investment = 45000 × 4 + 60000 × 8 = ₹6,60,000
Profit sharing ratio = 340:340:660 = 17:17:33
A's share = (17/67) × 30000 = ₹7,611.94
B's share = (17/67) × 30000 = ₹7,611.94
C's share = (33/67) × 30000 = ₹14,776.12
Q3.
A and B start a business with ₹40,000 and ₹60,000 respectively. After 3 months, C joins with ₹50,000. If the total profit is ₹35,000, find their shares.
Solution:
A's investment = 40000 × 12 = ₹4,80,000
B's investment = 60000 × 12 = ₹7,20,000
C's investment = 50000 × 9 = ₹4,50,000
Profit sharing ratio = 480:720:450 = 16:24:15
A's share = (16/55) × 35000 = ₹10,181.82
B's share = (24/55) × 35000 = ₹15,272.73
C's share = (15/55) × 35000 = ₹9,545.45
Q4.
A, B, and C start a business with ₹30,000, ₹40,000, and ₹50,000 respectively. After 5 months, A withdraws ₹10,000, B adds ₹20,000, and C withdraws ₹15,000. If the total profit is ₹40,000, find their shares.
Solution:
A's investment = 30000 × 5 + 20000 × 7 = ₹2,90,000
B's investment = 40000 × 5 + 60000 × 7 = ₹6,20,000
C's investment = 50000 × 5 + 35000 × 7 = ₹4,95,000
Profit sharing ratio = 290:620:495 = 58:124:99
A's share = (58/281) × 40000 = ₹8,256.23
B's share = (124/281) × 40000 = ₹17,651.25
C's share = (99/281) × 40000 = ₹14,092.52
Special Scenarios:
Example 7: Special Cases
Q1. A, B, and C invest ₹20,000 each for 1 year. If the total profit is ₹30,000, find their shares.
Solution:
Equal capital for equal time
Profit sharing ratio = 1:1:1
Each gets ₹10,000
Q2. A, B, and C invest ₹30,000 each for 4 months, 6 months, and 8 months respectively. If the total profit is ₹25,000, find their shares.
Solution:
Equal capital for different time
Profit sharing ratio = 4:6:8 = 2:3:4
A's share = (2/9) × 25000 = ₹5,556
B's share = (3/9) × 25000 = ₹8,333
C's share = (4/9) × 25000 = ₹11,111
Q3. A, B, and C invest ₹20,000, ₹30,000, and ₹40,000 for 1 year each. If the total profit is ₹30,000, find their shares.
Solution:
Different capital for equal time
Profit sharing ratio = 20000:30000:40000 = 2:3:4
A's share = (2/9) × 30000 = ₹6,667
B's share = (3/9) × 30000 = ₹10,000
C's share = (4/9) × 30000 = ₹13,333
Q4. A (working partner) and B (sleeping partner) invest ₹25,000 each for 1 year. A gets ₹10,000 as salary. If the total profit is ₹35,000, find their shares.
Solution:
Equal capital for equal time
Remaining profit = 35000 - 10000 = ₹25,000
Profit sharing ratio = 1:1
A's share = 10000 + 12500 = ₹22,500
B's share = ₹12,500
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