Partnership
Business Arithmetic. Master the relation between Capital, Time, and Profit ($P = C \times T$) and handle Active/Sleeping partners.
1. The Fundamental Law
Profit Ratio = (Capital Time) Ratio.
- Formula: .
- If Time is same: Profit Capital.
- If Capital is same: Profit Time.
Example:
Q: A invests 20k for 1 year. B 30k for 1 year.
Solution: .
2. The 'Month-Ratio' Method
When capitals change mid-year (e.g., adding/withdrawing money).
- Method: Calculate 'Month-Equivalent Capital'.
Example:
Q: A invests 1000. After 4 months, adds 500. Total year.
Solution: .
3. Active vs Sleeping Partner
Active partner gets salary/commission, Rest profit is shared.
- Equation: Net Shared Profit = Total Profit - (Salary + Commission).
- This Net Profit is then split by ratio.
Example:
Q: Total Profit 1000. A gets 10% for management. Ratio A:B is 1:1.
Solution: Management Fee: 100. Distributable: 900.
A gets . B gets 450.
A gets . B gets 450.
4. Working Backwards
Finding Capital or Time from Profit Ratio.
- Capital Ratio: .
- Time Ratio: .
Example:
Q: Profit 2:3. Capital 1:2. Find Time Ratio.
Solution: .
5. Donation & Reserve Fund
Often x% is donated or kept as reserve.
- Logic: Distribute only of the Total Profit amongst partners.
Example:
Q: Profit 2000. 10% to charity. A:B is 3:2.
Solution: Distributable = 90% of 2000 = 1800.
A = .
A = .
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