P invests ₹ 9100, for 3 months, Q invests ₹6825 for 2 months and R ₹8190 for 5 months in a business, If the total profit amounts to ₹ 4158, how much profit should Q get ?

Options

A. ₹ 346.50
B. ₹ 693
C. ₹ 682.50
D. ₹ 1386

Answer

To solve the problem, we need to calculate the profit share for Q based on the investments made by P, Q, and R, and the duration of their investments.

### Step-by-Step Solution:

1. **Calculate the Investment Amounts in Terms of Months:**
- For P:
\[ \text{Investment} = 9100 \text{ (amount)} \times 3 \text{ (months)} = 27300 \]
- For Q:
\[ \text{Investment} = 6825 \text{ (amount)} \times 2 \text{ (months)} = 13650 \]
- For R:
\[ \text{Investment} = 8190 \text{ (amount)} \times 5 \text{ (months)} = 40950 \]

2. **Determine the Total Investment:**
- Total investment = Investment of P + Investment of Q + Investment of R
\[ \text{Total Investment} = 27300 + 13650 + 40950 = 81900 \]

3. **Calculate the Ratio of Investments:**
- The ratio of the investments (P : Q : R) can be simplified as follows:
\[ \text{Ratio} = 27300 : 13650 : 40950 \]
- Dividing each term by 13650:
\[ \text{Ratio} = \frac{27300}{13650} : 1 : \frac{40950}{13650} = 2 : 1 : 3 \]

4. **Calculate the Total Parts in the Ratio:**
- Total parts = 2 + 1 + 3 = 6 parts.

5. **Determine the Profit Share for Q:**
- Total profit = ₹4158
- Profit per part = Total profit / Total parts
\[ \text{Profit per part} = \frac{4158}{6} = 693 \]
- Since Q has 1 part, Q's profit = 1 part × Profit per part
\[ \text{Q's Profit} = 1 \times 693 = 693 \]

### Final Answer:
Q should get a profit of ₹693.