A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs.6500 for 6 months, B invest Rs.8400 for 5 months and C invest Rs.10000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs.7400. Calculate the share of B in the profit.

Options

A. A. Rs 7500
B. B. Rs 2660
C. C. Rs 2800
D. D. Rs 2840

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the capital contribution of each partner.
- A's investment: Rs. 6500 for 6 months
- B's investment: Rs. 8400 for 5 months
- C's investment: Rs. 10000 for 3 months

### Step 2: Calculate the effective capital contribution (Capital × Time) for each partner.
- A's effective capital = 6500 × 6 = Rs. 39000
- B's effective capital = 8400 × 5 = Rs. 42000
- C's effective capital = 10000 × 3 = Rs. 30000

### Step 3: Determine the total effective capital.
Total effective capital = A's effective capital + B's effective capital + C's effective capital
= 39000 + 42000 + 30000 = Rs. 111000

### Step 4: Calculate the profit share ratio based on effective capital.
The ratio of their investments (effective capital) is:
- A : B : C = 39000 : 42000 : 30000

To simplify this ratio, we can divide each term by 3000:
- A : B : C = 13 : 14 : 10

### Step 5: Calculate A's share of the profit for being the working member.
Total profit = Rs. 7400
A's share for being the working member = 5% of total profit
= 5/100 × 7400 = Rs. 370

### Step 6: Calculate the remaining profit after A's share.
Remaining profit = Total profit - A's share
= 7400 - 370 = Rs. 7030

### Step 7: Calculate B's share of the remaining profit.
B's share of the remaining profit is based on the ratio of their investments:
- Total ratio parts = 13 + 14 + 10 = 37
- B's share = (B's ratio / Total ratio) × Remaining profit
= (14 / 37) × 7030

Calculating B's share:
= (14 × 7030) / 37
= 98420 / 37
= Rs. 2660

### Final Answer:
B's share in the profit is Rs. 2660.

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