Arun and Varun started business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, Akhil joined them with Rs. 20,000. What will be Varun's share in the total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business ?

Options

A. A) Rs. 7500
B. B) Rs. 4520
C. C) Rs. 8750
D. D) Rs. 6350

Answer

To find Varun's share in the total profit of Rs. 25,000 earned at the end of 2 years, we will follow these steps:

### Step 1: Calculate the investment duration for each partner.
- **Arun** invested Rs. 20,000 for 2 years (24 months).
- **Varun** invested Rs. 15,000 for 2 years (24 months).
- **Akhil** invested Rs. 20,000 but joined after 6 months, so he invested for 1.5 years (18 months).

### Step 2: Calculate the capital contribution of each partner in terms of "capital-months."
- **Arun's capital-months** = Investment × Duration = 20,000 × 24 = 480,000
- **Varun's capital-months** = Investment × Duration = 15,000 × 24 = 360,000
- **Akhil's capital-months** = Investment × Duration = 20,000 × 18 = 360,000

### Step 3: Find the total capital-months contributed by all partners.
Total capital-months = Arun's capital-months + Varun's capital-months + Akhil's capital-months
= 480,000 + 360,000 + 360,000 = 1,200,000

### Step 4: Determine the ratio of each partner's capital-months.
- **Arun's ratio** = 480,000 / 1,200,000 = 2/5
- **Varun's ratio** = 360,000 / 1,200,000 = 3/10
- **Akhil's ratio** = 360,000 / 1,200,000 = 3/10

### Step 5: Calculate Varun's share of the total profit.
Total profit = Rs. 25,000
Varun's share = (Varun's ratio) × (Total profit)
= (3/10) × 25,000
= 7,500

### Conclusion:
Varun's share in the total profit is Rs. 7,500.

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