A started a business with Rs. 52000 and after 4 months B joined him with Rs. 39000. At the end of the year out of the total profits B received total Rs. 20000 including 25% of the profits as commission for managing the business. What amount did A receive?

Answer

To solve the problem step by step, we will calculate the amount A received from the total profits after B joined the business.

### Step 1: Calculate the time of investment for A and B
- A invested Rs. 52,000 for 12 months (1 year).
- B invested Rs. 39,000 for 8 months (since he joined after 4 months).

### Step 2: Calculate the effective capital contribution of A and B
- A's contribution = Investment × Time = 52000 × 12 = 624000
- B's contribution = Investment × Time = 39000 × 8 = 312000

### Step 3: Calculate the total effective capital contribution
- Total contribution = A's contribution + B's contribution = 624000 + 312000 = 936000

### Step 4: Determine the profit-sharing ratio
- A's share of profit = A's contribution / Total contribution = 624000 / 936000 = 2/3
- B's share of profit = B's contribution / Total contribution = 312000 / 936000 = 1/3

### Step 5: Determine the total profit
- Let the total profit be P. According to the problem, B received Rs. 20,000, which includes 25% of the total profit as commission.
- Therefore, 25% of P = B's commission = 20000 - (75% of B's share of profit).

### Step 6: Calculate B's share of profit
- B's share of profit = 1/3 of (75% of P) = (1/3) * (0.75P) = 0.25P.
- B received Rs. 20,000, thus:
0.25P + 0.25P = 20000
0.5P = 20000
P = 20000 / 0.5 = 40000.

### Step 7: Calculate A's share of profit
- A's share of profit = (2/3) of (75% of P) = (2/3) * (0.75 * 40000) = (2/3) * 30000 = 20000.

### Step 8: Calculate A's total amount received
- A's total amount received = A's share of profit + (25% of total profit as commission).
- A's total amount = 20000 + (0.25 * 40000) = 20000 + 10000 = 30000.

### Final Answer:
A received Rs. 30,000.

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