Rahul started a business by investing Rs 45,000 . 6 months later Sanjay joined him with Rs `30,000` . In what ratio should the earned profit be distributed at the end of the year ?

Options

A. `1:3`
B. `3:1`
C. `2:3`
D. `3:2`

Answer

To solve the problem of how the profit should be distributed between Rahul and Sanjay, we can follow these steps:

### Step 1: Identify the investments and the time period
- Rahul's investment: Rs. 45,000
- Sanjay's investment: Rs. 30,000
- Time period for Rahul: 12 months (1 year)
- Time period for Sanjay: 6 months (since he joined 6 months later)

### Step 2: Calculate the capital contribution of each partner
To find out how much each partner contributed to the business in terms of "capital months," we multiply their investment by the time period for which it was invested.

- **Rahul's capital contribution** = Investment × Time = Rs. 45,000 × 12 months = Rs. 540,000
- **Sanjay's capital contribution** = Investment × Time = Rs. 30,000 × 6 months = Rs. 180,000

### Step 3: Determine the ratio of their capital contributions
Now, we will find the ratio of the capital contributions of Rahul and Sanjay.

- Ratio = Rahul's capital contribution : Sanjay's capital contribution
- Ratio = 540,000 : 180,000

To simplify the ratio, we can divide both sides by 180,000:

- Ratio = 540,000 ÷ 180,000 : 180,000 ÷ 180,000
- Ratio = 3 : 1

### Step 4: Conclusion
The profit earned at the end of the year should be distributed in the ratio of 3:1 between Rahul and Sanjay.

### Final Answer
The ratio in which the earned profit should be distributed is **3:1**.

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