Amit and Deepak started a business with initial investments in the ratio of `3:1` respectively . At the end of 8 months from start of the business ,Amit left . If Deepak received Rs 8000 as his share of the annual profit , then find what was annual profit ?

Options

A. A)Rs 2000
B. B)Rs 28000
C. C)Rs 24000
D. D)Rs 32000

Answer

To solve the problem, let's break it down step by step:

### Step 1: Understand the Initial Investment
Amit and Deepak started a business with their investments in the ratio of 3:1. This means if Amit invested 3 parts, Deepak invested 1 part.

### Step 2: Determine the Time of Investment
Amit stayed in the business for 8 months, while Deepak continued for the entire year (12 months).

### Step 3: Calculate the Effective Investment
To find out the effective investment of each partner, we multiply their investment by the time they invested:

- Amit's effective investment = Investment × Time = 3 parts × 8 months = 24 part-months
- Deepak's effective investment = Investment × Time = 1 part × 12 months = 12 part-months

### Step 4: Find the Ratio of Effective Investments
Now we can find the ratio of their effective investments:

- Amit's effective investment = 24 part-months
- Deepak's effective investment = 12 part-months

The ratio of Amit's to Deepak's effective investments is:
\[ \text{Ratio} = \frac{24}{12} = 2:1 \]

### Step 5: Determine the Profit Sharing Ratio
From the effective investment ratio, we can conclude that for every 3 parts of profit, Amit receives 2 parts and Deepak receives 1 part.

### Step 6: Use Deepak's Share to Find Total Profit
According to the problem, Deepak received Rs 8000 as his share of the profit, which corresponds to 1 part of the profit.

Let the total profit be represented as 3 parts (2 parts for Amit and 1 part for Deepak).

### Step 7: Calculate the Total Profit
If Deepak's share (1 part) is Rs 8000, then the total profit (3 parts) can be calculated as:
\[ \text{Total Profit} = 3 \times 8000 = Rs 24000 \]

### Conclusion
The annual profit of the business is Rs 24000.

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