A and B entered a partnership investing X 16000 and X 12000, respectively. After 3 months A takes out X 5000, while B puts in X 5000 more. After 3 months more. C joins the business with a capital of X 21000. After a year, they earned a profit of X 13200. By what value does the share of B exceeds the share of C ?

Options

A. X 1600
B. X 1800
C. X 2100
D. X 2300

Answer

To solve the problem step by step, we will calculate the effective capital contribution of A, B, and C over the year and then determine their respective shares of the profit.

### Step 1: Calculate A's effective capital contribution
- A invests ₹16,000 for the first 3 months.
- After 3 months, A withdraws ₹5,000, leaving A with ₹11,000 for the remaining 9 months.

**Calculation:**
- Contribution for the first 3 months:
\[ 16,000 \times 3 = 48,000 \]
- Contribution for the next 9 months:
\[ 11,000 \times 9 = 99,000 \]
- Total contribution of A:
\[ 48,000 + 99,000 = 147,000 \]

### Step 2: Calculate B's effective capital contribution
- B invests ₹12,000 for the first 3 months.
- After 3 months, B adds ₹5,000, making B's total investment ₹17,000 for the remaining 9 months.

**Calculation:**
- Contribution for the first 3 months:
\[ 12,000 \times 3 = 36,000 \]
- Contribution for the next 9 months:
\[ 17,000 \times 9 = 153,000 \]
- Total contribution of B:
\[ 36,000 + 153,000 = 189,000 \]

### Step 3: Calculate C's effective capital contribution
- C joins after 6 months with an investment of ₹21,000 for the last 6 months.

**Calculation:**
- Contribution for 6 months:
\[ 21,000 \times 6 = 126,000 \]

### Step 4: Calculate the total contributions and the ratio
Now we have the total contributions:
- A: ₹147,000
- B: ₹189,000
- C: ₹126,000

**Total contributions:**
\[ 147,000 + 189,000 + 126,000 = 462,000 \]

### Step 5: Calculate the profit share for each partner
The total profit is ₹13,200. We need to find the share of each partner based on their contributions.

**Total ratio of contributions:**
- A : B : C = 147,000 : 189,000 : 126,000

To simplify this ratio:
- Divide each term by 21,000:
- A: \( \frac{147,000}{21,000} = 7 \)
- B: \( \frac{189,000}{21,000} = 9 \)
- C: \( \frac{126,000}{21,000} = 6 \)

Thus, the ratio of A : B : C = 7 : 9 : 6.

### Step 6: Calculate each partner's share of the profit
- Total parts = 7 + 9 + 6 = 22

**A's share:**
\[ \text{A's share} = \frac{7}{22} \times 13,200 = 4,200 \]

**B's share:**
\[ \text{B's share} = \frac{9}{22} \times 13,200 = 5,400 \]

**C's share:**
\[ \text{C's share} = \frac{6}{22} \times 13,200 = 3,600 \]

### Step 7: Calculate by how much B's share exceeds C's share
To find out by how much B's share exceeds C's share:
\[ \text{B's share} - \text{C's share} = 5,400 - 3,600 = 1,800 \]

### Final Answer
B's share exceeds C's share by ₹1,800.

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