Partnership
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Solved Examples
Study MaterialSolved Examples – Partnership
Solved examples help students understand the practical application of Partnership concepts in competitive examinations. These examples are designed from basic to advanced level and cover important partnership problems frequently asked in SSC, Banking, Railway, CDS, NDA, CAT, UPSC, and placement aptitude tests.
Topics Covered in Solved Examples
- Simple Partnership Problems
- Compound Partnership Problems
- Capital and Time Ratio Problems
- Profit Sharing Problems
- Admission of New Partner
- Salary and Commission Cases
- Withdrawal and Additional Investment
- Partnership with Different Time Periods
- Business Profit Distribution
- Advanced Partnership Applications
Example 1: Simple Partnership Problem
Question: A and B invest 20000 and 30000 respectively in a business. Find their profit-sharing ratio.
Solution:
Both investments are for the same duration.
Profit ratio:
= 20000 : 30000
= 2 : 3
Therefore:
Profit-sharing ratio = 2 : 3
Example 2: Partnership with Different Time Periods
Question: A invests 10000 for 12 months and B invests 15000 for 8 months. Find their profit-sharing ratio.
Solution:
Profit ratio:
= 10000 × 12 : 15000 × 8
= 120000 : 120000
= 1 : 1
Therefore:
Profit-sharing ratio = 1 : 1
Example 3: Profit Distribution
Question: A and B share profit in the ratio 3 : 5. If total profit is 32000, find their individual shares.
Solution:
Total ratio parts:
= 3 + 5
= 8
A's share:
= (3/8) × 32000
= 12000
B's share:
= (5/8) × 32000
= 20000
Therefore:
A's share = 12000
B's share = 20000
Example 4: Same Capital Different Time
Question: A and B invest equal amounts in a business. A invests for 12 months while B invests for 8 months. Find the profit-sharing ratio.
Solution:
Since capitals are equal:
Profit ratio = Time ratio
= 12 : 8
= 3 : 2
Therefore:
Profit-sharing ratio = 3 : 2
Example 5: Finding Total Profit
Question: A's share in a business profit is 18000 and the ratio of A and B is 3 : 5. Find the total profit.
Solution:
A's 3 parts = 18000
1 part:
= 18000/3
= 6000
Total parts:
= 3 + 5
= 8
Total profit:
= 8 × 6000
= 48000
Therefore:
Total profit = 48000
Example 6: Admission of New Partner
Question: A invests 24000 for 12 months. After 4 months, B joins with 18000. Find the profit-sharing ratio.
Solution:
A's contribution:
= 24000 × 12
= 288000
B joins after 4 months, so invests for:
= 8 months
B's contribution:
= 18000 × 8
= 144000
Ratio:
= 288000 : 144000
= 2 : 1
Therefore:
Profit-sharing ratio = 2 : 1
Example 7: Partnership with Salary
Question: A and B share profit in the ratio 2 : 3. A receives a salary of 10000 from the total profit of 60000. Find B's share.
Solution:
Remaining profit after salary:
= 60000 − 10000
= 50000
Total ratio parts:
= 2 + 3
= 5
B's share:
= (3/5) × 50000
= 30000
Therefore:
B's share = 30000
Example 8: Partnership with Commission
Question: A and B share profits in the ratio 3 : 2. A receives a commission of 5000 from total profit of 55000. Find A's total amount.
Solution:
Remaining profit:
= 55000 − 5000
= 50000
A's profit share:
= (3/5) × 50000
= 30000
Total amount received by A:
= 30000 + 5000
= 35000
Therefore:
A receives = 35000
Example 9: Withdrawal of Capital
Question: A invests 20000 for first 6 months and withdraws half of it for remaining 6 months. Find his effective capital.
Solution:
First 6 months:
= 20000 × 6
= 120000
Remaining capital:
= 10000
Next 6 months:
= 10000 × 6
= 60000
Effective capital:
= 120000 + 60000
= 180000
Therefore:
Effective capital = 180000
Example 10: Additional Investment Problem
Question: A invests 15000 initially and adds 5000 after 4 months. Find his effective capital for the year.
Solution:
First investment:
= 15000 × 12
= 180000
Additional investment remains for:
= 8 months
Additional contribution:
= 5000 × 8
= 40000
Effective capital:
= 180000 + 40000
= 220000
Therefore:
Effective capital = 220000
Example 11: Compound Partnership Problem
Question: A invests 40000 for 8 months and B invests 30000 for 12 months. Find their profit-sharing ratio.
Solution:
A's contribution:
= 40000 × 8
= 320000
B's contribution:
= 30000 × 12
= 360000
Ratio:
= 320000 : 360000
= 8 : 9
Therefore:
Profit-sharing ratio = 8 : 9
Example 12: Three Partner Problem
Question: A, B, and C invest 10000, 15000, and 25000 respectively. Find their profit-sharing ratio.
Solution:
Ratio:
= 10000 : 15000 : 25000
= 2 : 3 : 5
Therefore:
Profit-sharing ratio = 2 : 3 : 5
Example 13: Three Partners with Different Time
Question: A invests 12000 for 12 months, B invests 15000 for 8 months, and C invests 10000 for 6 months. Find their profit-sharing ratio.
Solution:
A's contribution:
= 12000 × 12
= 144000
B's contribution:
= 15000 × 8
= 120000
C's contribution:
= 10000 × 6
= 60000
Ratio:
= 144000 : 120000 : 60000
= 12 : 10 : 5
= 6 : 5 : 2.5
= 12 : 10 : 5
Therefore:
Profit-sharing ratio = 12 : 10 : 5
Example 14: Finding Unknown Investment
Question: A and B share profit in ratio 2 : 3. A invested 20000 for whole year. Find B's investment if he invested for the whole year.
Solution:
Same investment period:
Investment ratio = Profit ratio
2 : 3 = 20000 : x
2x = 60000
x = 30000
Therefore:
B's investment = 30000
Example 15: Finding Unknown Time
Question: A and B invest equal amounts. Their profit ratio is 3 : 2. If A invested for 12 months, for how many months did B invest?
Solution:
Since capitals are equal:
Profit ratio = Time ratio
3 : 2 = 12 : x
3x = 24
x = 8
Therefore:
B invested for 8 months
Example 16: Partnership with Bonus
Question: Total business profit is 80000. A gets a bonus of 10000 and remaining profit is divided between A and B in ratio 3 : 5. Find B's share.
Solution:
Remaining profit:
= 80000 − 10000
= 70000
B's share:
= (5/8) × 70000
= 43750
Therefore:
B's share = 43750
Example 17: Effective Capital Method
Question: A invests 30000 for first 4 months and 50000 for next 8 months. Find his effective capital.
Solution:
First contribution:
= 30000 × 4
= 120000
Second contribution:
= 50000 × 8
= 400000
Effective capital:
= 120000 + 400000
= 520000
Therefore:
Effective capital = 520000
Example 18: Advanced Partnership Problem
Question: A, B, and C start a business investing 40000, 30000, and 50000 respectively. After 4 months, C withdraws half his investment. Find their profit-sharing ratio after one year.
Solution:
A's contribution:
= 40000 × 12
= 480000
B's contribution:
= 30000 × 12
= 360000
C's contribution:
First 4 months:
= 50000 × 4
= 200000
Remaining 8 months:
= 25000 × 8
= 200000
Total for C:
= 400000
Ratio:
= 480000 : 360000 : 400000
= 12 : 9 : 10
Therefore:
Profit-sharing ratio = 12 : 9 : 10
Important Exam Tips
- Always use Capital × Time method.
- Convert years into months whenever necessary.
- Simplify ratios carefully before final calculations.
- Deduct salary, bonus, or commission before profit distribution.
- Practice new partner admission questions regularly.
- Use fraction method for quick profit shares.
- Verify final ratios carefully.
Practicing solved examples regularly improves conceptual clarity, logical thinking, and calculation speed in solving Partnership questions in competitive examinations.