A and B entered into a partnership with investments of 15000 and 40000 respectively. After 3 months A left from the business, at the same time C joins with 30000. At the end of 9 months, they got 7800 as profit. Find the share of B.

Options

A. `'4800`
B. `'600`
C. `'2400`
D. `'1200`

Answer

To find the share of B in the partnership, we will follow these steps:

### Step 1: Determine the investments and time for each partner
- **A's investment**: ₹15,000 for 3 months
- **B's investment**: ₹40,000 for 9 months (B stays for the full duration)
- **C's investment**: ₹30,000 for 6 months (C joins after 3 months)

### Step 2: Calculate the effective capital contribution for each partner
To find the effective capital contribution, we multiply the investment by the time for each partner:
- **A's contribution**:
\[ 15,000 \times 3 = 45,000 \]
- **B's contribution**:
\[ 40,000 \times 9 = 360,000 \]
- **C's contribution**:
\[ 30,000 \times 6 = 180,000 \]

### Step 3: Write the contributions in ratio form
Now we can express the contributions in a ratio:
- A : B : C = 45,000 : 360,000 : 180,000

### Step 4: Simplify the ratio
To simplify the ratio, we can divide each term by 45,000:
- A : B : C = 1 : 8 : 4

### Step 5: Calculate the total parts of the ratio
Now, we find the total number of parts:
\[ 1 + 8 + 4 = 13 \]

### Step 6: Calculate B's share of the profit
The total profit is ₹7,800. To find B's share:
- B's part in the ratio is 8.
- B's share of the profit is calculated as:
\[ \text{B's share} = \left(\frac{8}{13}\right) \times 7,800 \]
Calculating this gives:
\[ \text{B's share} = \frac{8 \times 7,800}{13} = \frac{62,400}{13} = 4,800 \]

### Final Answer
Thus, B's share of the profit is ₹4,800.

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