A started a business by investing Rs. 8000. 3 months later B joined him with Rs. 5000. If at the end of a year total profit earned was Rs. 2350. How much is the share of A more than the share of B?

Options

A. Rs 600
B. Rs 800
C. RS 400
D. Rs 850

Answer

To solve the problem step by step, we will calculate the share of profit for both A and B based on their investments and the time they invested in the business.

### Step 1: Calculate the capital contribution of A and B
- A invested Rs. 8000 for 12 months.
- B invested Rs. 5000 for 9 months (since he joined 3 months later).

### Step 2: Calculate the effective capital for A and B
- Effective capital of A = Investment × Time = 8000 × 12 = Rs. 96000
- Effective capital of B = Investment × Time = 5000 × 9 = Rs. 45000

### Step 3: Find the ratio of their effective capital
- Ratio of A's capital to B's capital = 96000 : 45000
- Simplifying this ratio:
- Divide both sides by 15000:
- A : B = 32 : 15

### Step 4: Calculate the total profit
- Total profit earned = Rs. 2350

### Step 5: Calculate A's share of the profit
- Total parts = 32 + 15 = 47
- A's share = (A's ratio / Total parts) × Total profit
- A's share = (32 / 47) × 2350
- A's share = Rs. 1600

### Step 6: Calculate B's share of the profit
- B's share = (B's ratio / Total parts) × Total profit
- B's share = (15 / 47) × 2350
- B's share = Rs. 750

### Step 7: Calculate the difference between A's and B's share
- Difference = A's share - B's share
- Difference = 1600 - 750 = Rs. 850

### Final Answer
A's share is Rs. 850 more than B's share.

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