Three friends P, Q and R start a partnership business by investing in the ratio 5 : 4 : 2 respectively for a period of 3 years. The total amount invested is Rs. 22,000 and the profit earned at the end of 3 years is three eighths of the total investment. What amount does P receive as his share of the profit?

Introduction / Context:
This partnership problem gives the ratio of investments by three friends P, Q and R, the total amount invested, and the overall profit as a fraction of the total investment. Since all three invest for the same period of time, their shares of profit are proportional to their capital contributions. The question asks specifically for P's share of the profit.

Given Data / Assumptions:

• Investment ratio of P : Q : R is 5 : 4 : 2.
• Total amount invested is Rs. 22,000.
• Time period of investment for all three is 3 years (same for each partner).
• Profit earned at the end of 3 years is three eighths of the total investment.
• We must find P's share of the profit in rupees.

Concept / Approach:
Since all partners keep their money invested for the same duration, the profit distribution depends only on the ratio of their capital amounts. We first determine the total profit by taking three eighths of the total investment. Then we divide this profit among P, Q and R according to the ratio 5 : 4 : 2, which has 11 parts in total. P's share is 5 parts out of 11, so we compute that part of the total profit.

Step-by-Step Solution:
Step 1: Total investment is Rs. 22,000. Step 2: Profit at the end of 3 years is given as three eighths of the total investment. Step 3: Compute total profit: (3/8) * 22000 = 3 * 22000 / 8. Step 4: Calculate 22000 / 8 = 2750. So profit = 3 * 2750 = Rs. 8250. Step 5: Investment ratio of P : Q : R is 5 : 4 : 2, so the profit is divided in the same ratio. Step 6: Sum of the ratio parts is 5 + 4 + 2 = 11 parts. Step 7: Value of one part of profit is total profit / 11 = 8250 / 11 = Rs. 750. Step 8: P's share is 5 parts, so P receives 5 * 750 = Rs. 3750.

Verification / Alternative check:
Check the shares of Q and R as well. Q's share is 4 * 750 = Rs. 3000. R's share is 2 * 750 = Rs. 1500. Adding all three, 3750 + 3000 + 1500 = Rs. 8250, which matches the total profit computed from three eighths of Rs. 22,000. This confirms that the distribution is correct and that P's share of Rs. 3750 is accurate.

Why Other Options Are Wrong:
Amounts like Rs. 2750, Rs. 3000, Rs. 4000 or Rs. 3500 would give different combinations for Q and R that would not match the total profit of Rs. 8250 or would not maintain the required ratio of 5 : 4 : 2. For example, if P's share were Rs. 3000, then one part would be 3000 / 5 = 600, and the total would become 11 * 600 = Rs. 6600, which contradicts the correct total profit. Only Rs. 3750 yields a per part value of Rs. 750 and a correct total of Rs. 8250.

Common Pitfalls:
Some learners incorrectly try to compute each partner's investment from the total of Rs. 22,000 and then re-compute profit shares, which is unnecessary since the ratio is already given. Others may miscalculate three eighths of 22,000 or forget to divide by the sum of the ratio parts. Working step by step, first finding total profit and then dividing by the ratio, helps avoid such mistakes.

Final Answer:
P's share of the profit is Rs. 3750, which corresponds to option C.