Partnership Profit Calculation: Finding N's Share
This problem involves calculating the share of profit for a partner (N) in a business based on their investment and the duration of that investment over a year. We need to determine the effective investment made by both partners, M and N, considering changes in their capital during the year.
Investment Analysis for M and N
The profit share is proportional to the product of the investment amount and the time period (in months) for which the investment was made.
- M's Investment:
- Initial Investment: Rs. 2,00,000 for the first 4 months.
- Additional Investment: After 4 months, M adds Rs. 1,00,000, making the total Rs. 3,00,000 (Rs. 2,00,000 + Rs. 1,00,000). This amount is invested for the remaining 8 months (12 - 4 = 8).
- M's Equivalent Investment = (Rs. 2,00,000 \times 4) + (Rs. 3,00,000 \times 8)
- M's Equivalent Investment = Rs. 8,00,000 + Rs. 24,00,000 = Rs. 32,00,000
- N's Investment:
- Initial Investment: Rs. 3,00,000 for the first 4 months.
- Withdrawal: After 4 months, N withdraws Rs. 50,000, leaving Rs. 2,50,000 (Rs. 3,00,000 - Rs. 50,000). This amount is invested for the remaining 8 months.
- N's Equivalent Investment = (Rs. 3,00,000 \times 4) + (Rs. 2,50,000 \times 8)
- N's Equivalent Investment = Rs. 12,00,000 + Rs. 20,00,000 = Rs. 32,00,000
Profit Ratio Calculation
The ratio of their effective investments determines their profit-sharing ratio.
- Ratio M : N = M's Equivalent Investment : N's Equivalent Investment
- Ratio M : N = Rs. 32,00,000 : Rs. 32,00,000
- Simplified Ratio M : N = 1 : 1
N's Share of Profit
The total profit is Rs. 1,80,000. This profit is divided equally between M and N based on their 1:1 profit ratio.
- Total parts in the ratio = 1 + 1 = 2
- N's Share = (N's Ratio Part / Total Ratio Parts) \times Total Profit
- N's Share = (1 / 2) \times Rs. 1,80,000
- N's Share = Rs. 90,000
Therefore, N's share of the profit is Rs. 90,000.
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Important Questions from Partnership
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