Raj an and Sajan started a business initially with ? 14200 and ? 15600, respectively. If total profits at the end of years is X 74500, what is the Rajan's share in the profit?

Options

A. X 39000
B. X 39600
C. X 35000
D. X 35500

Answer

To find Rajan's share in the profit, we will follow these steps:

### Step 1: Determine the initial investments of Rajan and Sajan.
- Rajan's investment = Rs 14,200
- Sajan's investment = Rs 15,600

### Step 2: Calculate the profit-sharing ratio based on their investments.
- The profit-sharing ratio is calculated as:
\[ \text{Rajan's share} : \text{Sajan's share} = 14200 : 15600 \]

### Step 3: Simplify the ratio.
- We can simplify this ratio by dividing both amounts by 100 (removing the two zeros):
\[ 142 : 156 \]
- Next, we can further simplify this by dividing both numbers by 2:
\[ 71 : 78 \]
- Therefore, the profit-sharing ratio is 71:78.

### Step 4: Calculate the total parts in the ratio.
- Total parts = 71 + 78 = 149

### Step 5: Calculate Rajan's share of the total profit.
- Total profit = Rs 74,500
- Rajan's share of the profit can be calculated using the formula:
\[ \text{Rajan's share} = \frac{\text{Rajan's part}}{\text{Total parts}} \times \text{Total profit} \]
\[ \text{Rajan's share} = \frac{71}{149} \times 74500 \]

### Step 6: Perform the calculation.
- First, calculate \( \frac{74500}{149} \):
\[ \frac{74500}{149} = 500 \]
- Now, multiply by Rajan's part:
\[ \text{Rajan's share} = 500 \times 71 = 35500 \]

### Final Answer:
- Rajan's share in the profit is Rs 35,500.

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