Arun, Kamal and Vinay invested Rs. 8000, Rs. 4000 and Rs. 8000 respectively in a business. Arun left after six months. If after eight months, there was a gain of Rs. 4005, then what will be the share of Kamal ?

Options

A. Rs. 890
B. Rs. 1335
C. Rs. 1602
D. Rs. 1780

Answer

To solve the problem step by step, we will calculate the share of Kamal in the profit based on the investments made by Arun, Kamal, and Vinay.

### Step 1: Identify the investments and time periods
- Arun's investment = Rs. 8000
- Kamal's investment = Rs. 4000
- Vinay's investment = Rs. 8000

Arun invested for 6 months, while Kamal and Vinay invested for the full 8 months.

### Step 2: Calculate the effective capital contribution
To find the effective capital contribution, we multiply the investment by the time period for which it was invested.

- Arun's contribution = Investment × Time = 8000 × 6 = Rs. 48000
- Kamal's contribution = Investment × Time = 4000 × 8 = Rs. 32000
- Vinay's contribution = Investment × Time = 8000 × 8 = Rs. 64000

### Step 3: Calculate the total capital contribution
Now, we sum up the contributions of all three partners:
Total contribution = Arun's contribution + Kamal's contribution + Vinay's contribution
= 48000 + 32000 + 64000 = Rs. 144000

### Step 4: Calculate the ratio of their contributions
Now, we find the ratio of their contributions:
- Arun : Kamal : Vinay = 48000 : 32000 : 64000

To simplify this ratio, we can divide each term by 16000:
- Arun : Kamal : Vinay = 3 : 2 : 4

### Step 5: Calculate Kamal's share of the profit
The total profit from the business is Rs. 4005. We need to find Kamal's share based on the ratio we calculated.

First, find the total parts in the ratio:
Total parts = 3 + 2 + 4 = 9

Now, calculate Kamal's share:
Kamal's share = (Kamal's ratio / Total parts) × Total profit
= (2 / 9) × 4005

### Step 6: Calculate the final amount
Now, we compute Kamal's share:
Kamal's share = (2 / 9) × 4005 = 890

### Final Answer
Kamal's share of the profit is Rs. 890.

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