Divyaraj , Sameer and Ayush started a business each investing 20000 rs. After 4 months Divyaraj withdraws Rs. 6000, Sameer with draws 8000 and Ayush invest 6000 more .At end of year total profit was 65600 Rs. Find the share of Ayush ?

Options

A. A)19200 Rs
B. B)28800 Rs
C. C)28600 Rs
D. D)27600 Rs

Answer

To solve the problem step by step, we will calculate the profit share of Ayush based on the investments made by Divyaraj, Sameer, and Ayush throughout the year.

### Step 1: Initial Investment
Each of the three partners invested Rs. 20,000 at the beginning.

- Divyaraj's initial investment = Rs. 20,000
- Sameer's initial investment = Rs. 20,000
- Ayush's initial investment = Rs. 20,000

### Step 2: Calculate the Effective Investment Period
- Divyaraj and Sameer invested for 12 months.
- Ayush invested for 12 months as well, but he added Rs. 6,000 after 4 months.

### Step 3: Adjust Investments After 4 Months
After 4 months:
- Divyaraj withdraws Rs. 6,000, leaving him with Rs. 14,000.
- Sameer withdraws Rs. 8,000, leaving him with Rs. 12,000.
- Ayush adds Rs. 6,000, increasing his total to Rs. 26,000.

### Step 4: Calculate the Contribution in Terms of Money-Months
- **Divyaraj's contribution:**
- For the first 4 months: 20,000 * 4 = 80,000
- For the next 8 months: 14,000 * 8 = 112,000
- Total = 80,000 + 112,000 = 192,000

- **Sameer's contribution:**
- For the first 4 months: 20,000 * 4 = 80,000
- For the next 8 months: 12,000 * 8 = 96,000
- Total = 80,000 + 96,000 = 176,000

- **Ayush's contribution:**
- For the first 4 months: 20,000 * 4 = 80,000
- For the next 8 months: 26,000 * 8 = 208,000
- Total = 80,000 + 208,000 = 288,000

### Step 5: Calculate the Total Contribution
- Total contributions:
- Divyaraj = 192,000
- Sameer = 176,000
- Ayush = 288,000

### Step 6: Calculate the Ratio of Contributions
Now we can find the ratio of their contributions:
- Divyaraj : Sameer : Ayush = 192,000 : 176,000 : 288,000

To simplify:
- Divide each by 16,000:
- Divyaraj = 12
- Sameer = 11
- Ayush = 18

Thus, the ratio is:
- Divyaraj : Sameer : Ayush = 12 : 11 : 18

### Step 7: Calculate the Total Profit
The total profit at the end of the year is Rs. 65,600.

### Step 8: Calculate the Value of Each Part
Total parts = 12 + 11 + 18 = 41 parts.

Value of each part = Total Profit / Total Parts = 65,600 / 41 = 1,600.

### Step 9: Calculate Ayush's Share
Ayush's share = 18 parts = 18 * 1,600 = Rs. 28,800.

### Final Answer
Ayush's share of the profit is Rs. 28,800.

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