Praveen started a shop investing Rs. 18,000/- Six months later Naveen joined him investing RS 16,000/- If at the end of year they made a profit of Rs. 5,200/-What will be Naveen's share in it?

Options

A. Rs. 800/-
B. Rs. 1,200/-
C. Rs 2000/-
D. Rs. 1600/-

Answer

To solve the problem of determining Naveen's share of the profit, we can follow these steps:

### Step 1: Determine the investment and time for each partner
- Praveen's investment: Rs. 18,000
- Time invested by Praveen: 12 months (since he started at the beginning of the year)
- Naveen's investment: Rs. 16,000
- Time invested by Naveen: 6 months (since he joined 6 months later)

### Step 2: Calculate the capital contribution in terms of "capital * time"
- For Praveen:
\[ \text{Capital contribution} = 18000 \times 12 = 216000 \]

- For Naveen:
\[ \text{Capital contribution} = 16000 \times 6 = 96000 \]

### Step 3: Find the ratio of their capital contributions
- The ratio of Praveen's contribution to Naveen's contribution is:
\[ \text{Ratio} = \frac{216000}{96000} = \frac{216}{96} = \frac{27}{12} = \frac{9}{4} \]

### Step 4: Assign profit shares based on the ratio
- Let Praveen's share of profit be \(9x\) and Naveen's share be \(4x\).
- Total profit = Rs. 5,200
- Therefore, the equation becomes:
\[ 9x + 4x = 5200 \]
\[ 13x = 5200 \]

### Step 5: Solve for \(x\)
- Divide both sides by 13:
\[ x = \frac{5200}{13} = 400 \]

### Step 6: Calculate Naveen's share
- Naveen's share of the profit:
\[ 4x = 4 \times 400 = 1600 \]

### Conclusion
Naveen's share in the profit is **Rs. 1,600**.

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