Aand B started a business by Investing Rs 25000 and Rs. 20000 respectively. B left the business after 7 months and C joined the business with a sum of Rs. 30000. The profit earned at the end of the year is Rs 76, 700 What is B's share of profit ?

Options

A. Rs 18.200
B. Rs.20,200
C. Rs.21,400
D. Rs 22,300

Answer

To find B's share of the profit, we will follow these steps:

### Step 1: Determine the investment and time for each partner
- A invests Rs 25,000 for 12 months.
- B invests Rs 20,000 for 7 months (leaves after 7 months).
- C joins with Rs 30,000 for the remaining 5 months (from month 7 to month 12).

### Step 2: Calculate the capital contribution in terms of "capital months"
- For A:
\[ \text{Capital months} = 25000 \times 12 = 300000 \]
- For B:
\[ \text{Capital months} = 20000 \times 7 = 140000 \]
- For C:
\[ \text{Capital months} = 30000 \times 5 = 150000 \]

### Step 3: Calculate the total capital months
\[ \text{Total Capital Months} = 300000 + 140000 + 150000 = 590000 \]

### Step 4: Find the ratio of capital contributions
- A's share:
\[ \text{A's share} = 300000 \]
- B's share:
\[ \text{B's share} = 140000 \]
- C's share:
\[ \text{C's share} = 150000 \]

The ratio of their contributions is:
\[ \text{A : B : C} = 300000 : 140000 : 150000 \]
To simplify, divide each term by 10000:
\[ \text{A : B : C} = 30 : 14 : 15 \]

### Step 5: Calculate the total parts in the ratio
\[ \text{Total parts} = 30 + 14 + 15 = 59 \]

### Step 6: Calculate the value of one part of the profit
Given the total profit is Rs 76,700:
\[ \text{Value of one part} = \frac{76700}{59} \approx 1300 \]

### Step 7: Calculate B's share of the profit
B's share in the ratio is 14 parts:
\[ \text{B's profit} = 14 \times 1300 = 18200 \]

### Final Answer
B's share of the profit is Rs 18,200.

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