P and Q starts a business with investment of ₹ 28000 and ₹ 42000 respectively. P invests for 8 months and Q invests for one year.If the total profit at the end of the year is ₹ 21125, then what is the share of P?

Options

A. ₹ 12625
B. ₹ 14625
C. ₹ 6500
D. ₹ 8750

Answer

To find the share of P in the profit from the business, we will follow these steps:

### Step 1: Determine the investments and time periods
- P's investment = ₹28,000 for 8 months
- Q's investment = ₹42,000 for 12 months (1 year)

### Step 2: Calculate the product of investment and time for both P and Q
- For P: Investment × Time = ₹28,000 × 8 months = ₹224,000
- For Q: Investment × Time = ₹42,000 × 12 months = ₹504,000

### Step 3: Find the ratio of P's and Q's contributions
- The ratio of P's contribution to Q's contribution is:
\[ \text{Ratio} = \frac{P's \, contribution}{Q's \, contribution} = \frac{224,000}{504,000} \]
- Simplifying this ratio:
\[ \text{Ratio} = \frac{224}{504} = \frac{4}{9} \]

### Step 4: Calculate the total parts of the profit
- The total parts in the ratio = 4 (for P) + 9 (for Q) = 13 parts.

### Step 5: Determine P's share of the total profit
- Total profit = ₹21,125
- P's share of the profit is calculated as:
\[ P's \, share = \left(\frac{4}{13}\right) \times 21,125 \]
- Calculating P's share:
\[ P's \, share = \frac{4 \times 21,125}{13} = \frac{84,500}{13} = 6,500 \]

### Conclusion
P's share of the profit is ₹6,500.

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