A and B enter into partnership investing Rs. 48,000 and Rs. 60,000 respectively. After 3 months, A withdraws Rs. 8,000 while B invests Rs. 6,000 after 6 months of starting of business. Out of the total amount of profit, if A gets Rs. 12,000 as his share at the end of the year total profit is :

Answer

To solve the problem step by step, we need to calculate the effective capital contribution of both A and B over the year and then determine the total profit based on A's share of the profit.

### Step 1: Calculate the effective capital contribution of A
- A's initial investment: Rs. 48,000 for the first 3 months.
- After 3 months, A withdraws Rs. 8,000, leaving him with Rs. 40,000 for the next 9 months.

**Calculation:**
- Contribution for the first 3 months:
\[ 48,000 \times 3 = 144,000 \]
- Contribution for the next 9 months:
\[ 40,000 \times 9 = 360,000 \]
- Total contribution of A:
\[ 144,000 + 360,000 = 504,000 \]

### Step 2: Calculate the effective capital contribution of B
- B's initial investment: Rs. 60,000 for the first 6 months.
- After 6 months, B invests an additional Rs. 6,000, making his total investment Rs. 66,000 for the next 6 months.

**Calculation:**
- Contribution for the first 6 months:
\[ 60,000 \times 6 = 360,000 \]
- Contribution for the next 6 months:
\[ 66,000 \times 6 = 396,000 \]
- Total contribution of B:
\[ 360,000 + 396,000 = 756,000 \]

### Step 3: Determine the ratio of contributions
Now we have the total contributions:
- A's total contribution: Rs. 504,000
- B's total contribution: Rs. 756,000

**Ratio of contributions:**
\[ \text{Ratio of A to B} = \frac{504,000}{756,000} = \frac{2}{3} \]

### Step 4: Calculate the total profit based on A's share
We know that A's share of the profit is Rs. 12,000. Since the ratio of their shares is 2:3, we can find B's share.

**Calculation of B's share:**
- A's share corresponds to 2 parts, and B's share corresponds to 3 parts.
- Total parts = 2 + 3 = 5 parts.
- Value of each part:
\[ \text{Value of 1 part} = \frac{12,000}{2} = 6,000 \]
- B's share:
\[ \text{B's share} = 3 \times 6,000 = 18,000 \]

### Step 5: Calculate the total profit
Total profit can be calculated by adding A's and B's shares:
\[ \text{Total profit} = A's share + B's share = 12,000 + 18,000 = 30,000 \]

### Final Answer
The total profit at the end of the year is **Rs. 30,000**.

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