N invested Rs. 20, 000 in a business , Six months later, C joined him with Rs. 10,000 At the end of the year , the profit was Rs. 10,000 what should be the share of N ?
A. 2,000
B. 4,000
C. 6,000
D. 8,000

Options

A. C
B. B
C. A
D. D

Answer

To find N's share of the profit, we can follow these steps:

### Step 1: Determine the Investment and Time for Each Partner
- N invested Rs. 20,000 for the entire year (12 months).
- C invested Rs. 10,000 but joined 6 months later, so he invested for only 6 months.

### Step 2: Calculate the Capital Contribution in Terms of Months
- N's contribution in terms of capital months = Investment × Time = 20,000 × 12 = 240,000.
- C's contribution in terms of capital months = Investment × Time = 10,000 × 6 = 60,000.

### Step 3: Find the Ratio of Their Contributions
- The ratio of N's contribution to C's contribution is:
\[ \text{Ratio of N to C} = \frac{240,000}{60,000} = \frac{4}{1} \]

### Step 4: Calculate Total Parts in the Profit Sharing
- Total parts = 4 (for N) + 1 (for C) = 5 parts.

### Step 5: Calculate N's Share of the Profit
- Total profit = Rs. 10,000.
- N's share = (N's parts / Total parts) × Total profit
\[ \text{N's share} = \left(\frac{4}{5}\right) \times 10,000 = 8,000. \]

### Conclusion
N's share of the profit is Rs. 8,000.

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