To solve the problem step by step, we need to calculate the profit shares of A, B, and C based on their investments and the time they invested.
### Step 1: Calculate the Capital Contribution of Each Partner
- **A's Investment**: Rs. 40,500 for 12 months.
- **B's Investment**: Rs. 45,000 for 12 months.
- **C's Investment**: Rs. 60,000 for the first 6 months, then Rs. 45,000 for the next 6 months (after withdrawing Rs. 15,000).
### Step 2: Calculate the Effective Capital for Each Partner
- **A's Effective Capital**:
\[
\text{A's Capital} = 40,500 \times 12 = 486,000
\]
- **B's Effective Capital**:
\[
\text{B's Capital} = 45,000 \times 12 = 540,000
\]
- **C's Effective Capital**:
\[
\text{C's Capital} = (60,000 \times 6) + (45,000 \times 6) = 360,000 + 270,000 = 630,000
\]
### Step 3: Calculate the Total Effective Capital
\[
\text{Total Capital} = A's Capital + B's Capital + C's Capital = 486,000 + 540,000 + 630,000 = 1,656,000
\]
### Step 4: Calculate the Profit Sharing Ratio
- The ratio of their effective capitals is:
\[
\text{Ratio} = A : B : C = 486,000 : 540,000 : 630,000
\]
To simplify this ratio, we can divide each term by 18,000:
- A: \( \frac{486,000}{18,000} = 27 \)
- B: \( \frac{540,000}{18,000} = 30 \)
- C: \( \frac{630,000}{18,000} = 35 \)
Thus, the simplified ratio is:
\[
A : B : C = 27 : 30 : 35
\]
### Step 5: Calculate the Total Parts in the Ratio
\[
\text{Total Parts} = 27 + 30 + 35 = 92
\]
### Step 6: Calculate Each Partner's Share of the Profit
Given the total profit is Rs. 56,100:
- **A's Share**:
\[
A's Share = \frac{27}{92} \times 56100 = 16,500
\]
- **B's Share**:
\[
B's Share = \frac{30}{92} \times 56100 = 18,300
\]
- **C's Share**:
\[
C's Share = \frac{35}{92} \times 56100 = 21,300
\]
### Step 7: Calculate the Difference Between C's and A's Share
To find how much C's share exceeds A's share:
\[
\text{Difference} = C's Share - A's Share = 21,300 - 16,500 = 4,800
\]
### Final Answer
C's share exceeds A's share by Rs. 4,800.
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