X and Y started a business by investing Rs. 171000 and Rs. 243000 respectively. If Xs share in the profit earned at the end of year is Rs. 3800, what will be the total profit (in Rs.) earned by them together?

Options

A. 9200
B. 9600
C. 8400
D. 8800

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Identify the investments of X and Y
- X's investment = Rs. 171,000
- Y's investment = Rs. 243,000

### Step 2: Calculate the ratio of their investments
- The ratio of X's investment to Y's investment can be calculated as:
\[ \text{Ratio} = \frac{171000}{243000} \]
- Simplifying this ratio:
\[ \text{Ratio} = \frac{171}{243} = \frac{19}{27} \]
(This is done by dividing both numbers by 9.)

### Step 3: Set the profit shares in the ratio of their investments
- Since the time period is the same for both, the profit will also be divided in the same ratio of their investments, which is 19:27.

### Step 4: Let the total profit be represented as TP
- Let the total profit be TP.
- X's share of the profit can be expressed as:
\[ \text{X's share} = \frac{19}{(19 + 27)} \times TP = \frac{19}{46} \times TP \]

### Step 5: Set up the equation with the given share of X
- We know that X's share in the profit is Rs. 3,800. Therefore:
\[ \frac{19}{46} \times TP = 3800 \]

### Step 6: Solve for TP
- To find TP, we can rearrange the equation:
\[ TP = 3800 \times \frac{46}{19} \]
- Calculate \( \frac{46}{19} \):
\[ \frac{46}{19} = 2.4211 \quad (\text{approximately}) \]
- Now, calculate TP:
\[ TP = 3800 \times 2.4211 \approx 9200 \]

### Conclusion
- The total profit earned by X and Y together is Rs. 9,200.

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