A starts business with Rs. 7000 and after 5 months, B joined as a partner. After a year the profit is divided in the ratlo 2:3. The capital of B is :

Options

A. Rs. 9,000
B. Rs. 10,000
C. Rs. 6,500
D. Rs. 18,000

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Understand the Problem
A starts a business with Rs. 7000 and B joins after 5 months. After a year, the profit is divided in the ratio of 2:3. We need to find the capital invested by B.

### Step 2: Determine the Time Period of Investment
- A invests Rs. 7000 for the entire year (12 months).
- B joins after 5 months, so B invests for 12 - 5 = 7 months.

### Step 3: Set Up the Profit Sharing Ratio
The profit is divided in the ratio of A's investment to B's investment:
- Let A's profit share be represented as 2 parts and B's profit share as 3 parts.

### Step 4: Calculate the Effective Investment
The profit share can be calculated using the formula:
\[ \text{Profit Share} = \text{Investment} \times \text{Time} \]
- For A:
\[ \text{A's investment} = 7000 \times 12 = 84000 \]
- For B: Let B's investment be \( B_I \).
\[ \text{B's investment} = B_I \times 7 \]

### Step 5: Set Up the Equation Based on the Ratio
According to the ratio of profit sharing:
\[ \frac{A's \, Profit}{B's \, Profit} = \frac{2}{3} \]
This can be written as:
\[ \frac{84000}{B_I \times 7} = \frac{2}{3} \]

### Step 6: Cross Multiply to Solve for \( B_I \)
Cross multiplying gives:
\[ 3 \times 84000 = 2 \times (B_I \times 7) \]
\[ 252000 = 14B_I \]

### Step 7: Solve for \( B_I \)
Now, divide both sides by 14:
\[ B_I = \frac{252000}{14} = 18000 \]

### Conclusion
The capital of B is Rs. 18000.