A started a business with Rs. 52,000 and after 4 month B joined him with Rs. 39000. At the end of the year, out of the total profit B received total 20,000 including 25% of the profit as comission for managing the business. What amount did A receive?

Answer

To solve the problem, we need to determine how much A received from the total profit after B joined the business. Let's break it down step by step.

### Step 1: Calculate the capital contribution of A and B in terms of months.
- A started the business with Rs. 52,000 and invested this amount for 12 months.
- B joined after 4 months with Rs. 39,000, so B's investment was for 8 months (12 - 4 = 8).

### Step 2: Calculate the effective capital contribution.
- A's effective capital contribution = Rs. 52,000 * 12 months = Rs. 624,000.
- B's effective capital contribution = Rs. 39,000 * 8 months = Rs. 312,000.

### Step 3: Calculate the total effective capital contribution.
- Total effective capital contribution = A's contribution + B's contribution
= Rs. 624,000 + Rs. 312,000 = Rs. 936,000.

### Step 4: Determine the profit-sharing ratio.
- A's share of the profit = A's effective contribution / Total effective contribution
= Rs. 624,000 / Rs. 936,000 = 2/3.
- B's share of the profit = B's effective contribution / Total effective contribution
= Rs. 312,000 / Rs. 936,000 = 1/3.

### Step 5: Calculate the total profit.
- B received Rs. 20,000, which includes a 25% commission for managing the business.
- Let the total profit be P. The commission received by B = 25% of P = 0.25P.
- Therefore, B's share of the profit = (1/3)P.
- We can set up the equation: (1/3)P + 0.25P = Rs. 20,000.

### Step 6: Solve for P.
- Convert 0.25P to a fraction: 0.25P = (1/4)P.
- Now we have: (1/3)P + (1/4)P = Rs. 20,000.
- To solve this, find a common denominator (which is 12):
- (4/12)P + (3/12)P = Rs. 20,000.
- (7/12)P = Rs. 20,000.
- Now, multiply both sides by (12/7):
- P = Rs. 20,000 * (12/7) = Rs. 34,285.71 (approximately).

### Step 7: Calculate A's share of the profit.
- A's share of the profit = (2/3) * P.
- A's share = (2/3) * Rs. 34,285.71 = Rs. 22,857.14 (approximately).

### Step 8: Final Amount Received by A.
- Therefore, A received approximately Rs. 22,857.14.