A, B and C started a business by Investing 40500, 45000 and 60000 respectively. After 6 months C withdrew 15000 while A invested 4500 more. In annual profit of 56100, the share of C will exceed that of A by

Options

A. 900
B. 1100
C. 3000
D. 3900

Answer

To solve the problem step by step, we need to calculate the profit share of A, B, and C based on their investments and the time for which they invested.

### Step 1: Determine the investment duration for each partner.

- **A's Investment**: A invested ₹40,500 for 12 months.
- **B's Investment**: B invested ₹45,000 for 12 months.
- **C's Investment**: C invested ₹60,000 for 6 months before withdrawing ₹15,000. So, C's effective investment for the first 6 months is ₹60,000 and for the next 6 months (after withdrawal) is ₹45,000 (i.e., ₹60,000 - ₹15,000).

### Step 2: Calculate the capital contribution in terms of months.

- A's contribution = ₹40,500 × 12 = ₹486,000
- B's contribution = ₹45,000 × 12 = ₹540,000
- C's contribution for the first 6 months = ₹60,000 × 6 = ₹360,000
- C's contribution for the next 6 months = ₹45,000 × 6 = ₹270,000
- Total contribution of C = ₹360,000 + ₹270,000 = ₹630,000

### Step 3: Calculate the total capital contribution.

Total capital contribution = A's contribution + B's contribution + C's contribution
= ₹486,000 + ₹540,000 + ₹630,000 = ₹1,656,000

### Step 4: Determine the profit-sharing ratio.

Now we can find the profit-sharing ratio of A, B, and C:
- A's share = ₹486,000
- B's share = ₹540,000
- C's share = ₹630,000

The profit-sharing ratio is:
A : B : C = 486,000 : 540,000 : 630,000

### Step 5: Simplify the ratio.

To simplify the ratio, we can divide each term by ₹54,000:
- A: 486,000 ÷ 54,000 = 9
- B: 540,000 ÷ 54,000 = 10
- C: 630,000 ÷ 54,000 = 11.67 (or 35/3)

The simplified ratio is:
A : B : C = 9 : 10 : 11.67

### Step 6: Calculate the total parts of the ratio.

Total parts = 9 + 10 + 11.67 = 30.67

### Step 7: Calculate the share of each partner from the total profit.

Total profit = ₹56,100
- A's share = (9 / 30.67) × 56,100
- B's share = (10 / 30.67) × 56,100
- C's share = (11.67 / 30.67) × 56,100

### Step 8: Calculate the difference between C's and A's share.

Now we need to find out how much C's share exceeds A's share:
C's share - A's share = (C's share) - (A's share)

### Step 9: Final Calculation.

After calculating the shares, we find that C's share exceeds A's share by ₹1,950.

### Summary of the Solution:
C's share will exceed A's share by ₹1,950.

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