A started a business with the capital of Rs. 1800. After 4 months B joined with Rs. 3600. 6 months after the business started C joined with Rs. 1200. If the total profit earned at the end of the year Is Rs. 1760, then what is the share (in Rs.) of A?

Options

A. 540
B. 660
C. 840
D. 720

Answer

To solve the problem, we need to calculate the share of profit for A based on the capital invested and the time for which it was invested. Here’s a step-by-step breakdown of the solution:

### Step 1: Calculate A's Investment Contribution
A started the business with a capital of Rs. 1800 and invested it for the entire year (12 months).

- **A's Contribution** = Capital × Time = 1800 × 12 = 21600

### Step 2: Calculate B's Investment Contribution
B joined the business after 4 months with a capital of Rs. 3600. Therefore, B invested for 8 months (12 - 4 = 8).

- **B's Contribution** = Capital × Time = 3600 × 8 = 28800

### Step 3: Calculate C's Investment Contribution
C joined the business after 6 months with a capital of Rs. 1200. Thus, C invested for 6 months (12 - 6 = 6).

- **C's Contribution** = Capital × Time = 1200 × 6 = 7200

### Step 4: Calculate Total Contributions
Now, we sum up the contributions of A, B, and C to find the total investment in terms of capital-months.

- **Total Contribution** = A's Contribution + B's Contribution + C's Contribution
- Total Contribution = 21600 + 28800 + 7200 = 57600

### Step 5: Calculate the Profit Sharing Ratio
Next, we find the ratio of their contributions:

- A : B : C = 21600 : 28800 : 7200

To simplify this ratio, we can divide each term by 7200:

- A : B : C = (21600 ÷ 7200) : (28800 ÷ 7200) : (7200 ÷ 7200)
- A : B : C = 3 : 4 : 1

### Step 6: Calculate the Total Parts in the Ratio
Now, we find the total parts in the ratio:

- Total parts = 3 + 4 + 1 = 8

### Step 7: Calculate the Value of Each Part
The total profit earned at the end of the year is Rs. 1760. To find the value of each part, we divide the total profit by the total parts:

- Value of each part = Total Profit / Total Parts = 1760 / 8 = 220

### Step 8: Calculate A's Share of the Profit
Finally, to find A's share of the profit, we multiply the value of each part by A's share in the ratio:

- A's Share = Value of each part × A's parts = 220 × 3 = 660

### Final Answer
A's share of the profit is Rs. 660.

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