A starts an Industry with 20 lakhs. After 4 months he enters Into a partnership with B who contributes 40 lakhs. C joins them after another 3 months with a capital of 60 lakhs. At the year end, the balance sheet shows a profit of 86000. Find the share of A in the profit.

Options

A. 32000
B. 24000
C. 18000
D. 16000

Answer

To solve the problem step by step, we will calculate the share of A in the profit based on the capital he invested and the duration for which he invested it.

### Step 1: Determine the time each partner invested their capital
- **A** invested for 12 months (since he started the industry).
- **B** invested for 8 months (he joined after 4 months).
- **C** invested for 5 months (he joined after 7 months).

### Step 2: Calculate the capital contribution of each partner
- **A's capital** = 20 lakhs
- **B's capital** = 40 lakhs
- **C's capital** = 60 lakhs

### Step 3: Calculate the capital-time product for each partner
- For **A**:
\[ \text{Capital-Time for A} = 20 \text{ lakhs} \times 12 \text{ months} = 240 \text{ lakh-months} \]

- For **B**:
\[ \text{Capital-Time for B} = 40 \text{ lakhs} \times 8 \text{ months} = 320 \text{ lakh-months} \]

- For **C**:
\[ \text{Capital-Time for C} = 60 \text{ lakhs} \times 5 \text{ months} = 300 \text{ lakh-months} \]

### Step 4: Calculate the total capital-time contribution
\[ \text{Total Capital-Time} = 240 + 320 + 300 = 860 \text{ lakh-months} \]

### Step 5: Determine the profit-sharing ratio
The profit-sharing ratio is based on the capital-time contributions:
- A's share = 240
- B's share = 320
- C's share = 300

Thus, the ratio of their contributions is:
\[ \text{Ratio} = A : B : C = 240 : 320 : 300 \]

### Step 6: Simplify the ratio
To simplify the ratio, we can divide each term by 20:
\[ A : B : C = 12 : 16 : 15 \]

### Step 7: Calculate the total parts in the ratio
\[ \text{Total parts} = 12 + 16 + 15 = 43 \]

### Step 8: Calculate the share of A in the profit
Given that the total profit is 86,000, we can find the share of A:
- First, find the value of one part:
\[ \text{Value of one part} = \frac{86000}{43} = 2000 \]

- Now, calculate A's share:
\[ \text{A's share} = 12 \times 2000 = 24000 \]

### Final Answer
Thus, A's share in the profit is **24,000**.

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