A and B enter into a partnership by investing ₹3750 and ₹4800 respectively. After 3months, C joined them with ₹4500. If the total profit earned by them after one year of partnership is ₹4452, what is the profit earned by B alone?

Options

A. ₹1186
B. ₹1458
C. ₹1792
D. ₹1324

Answer

To solve the problem, we need to determine the profit earned by B alone after one year of partnership. Here’s the step-by-step solution:

### Step 1: Calculate the investment duration for each partner.
- A invests ₹3750 for 12 months.
- B invests ₹4800 for 12 months.
- C invests ₹4500 for 9 months (since C joins after 3 months).

### Step 2: Calculate the capital contribution of each partner.
- A's contribution = 3750 * 12 = ₹45000
- B's contribution = 4800 * 12 = ₹57600
- C's contribution = 4500 * 9 = ₹40500

### Step 3: Calculate the total capital contribution.
Total capital = A's contribution + B's contribution + C's contribution
Total capital = ₹45000 + ₹57600 + ₹40500 = ₹143100

### Step 4: Calculate the profit-sharing ratio.
The profit-sharing ratio is based on the capital contributions:
- A's share = 45000 / 143100
- B's share = 57600 / 143100
- C's share = 40500 / 143100

### Step 5: Calculate the profit earned by B.
Total profit = ₹4452
B's profit = Total profit * (B's share of the ratio)
B's profit = ₹4452 * (57600 / 143100)

### Step 6: Simplify the calculation.
B's profit = ₹4452 * (57600 / 143100)
= ₹4452 * 0.402
= ₹1798.04 (approximately)

### Final Answer:
The profit earned by B alone is approximately ₹1798.04.

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