A starts business with Rs. 3500/- and after 5 months, B Joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is B's contribution in the capital?

Options

A. Rs. 8000/-
B. Rs. 8500/-
C. Rs. 9000/-
D. Rs. 7500/-

Answer

To solve the problem step by step, we will use the information given about A and B's investments and the profit-sharing ratio.

### Step 1: Understand the investments and time periods
- A starts the business with Rs. 3500 and invests for 12 months.
- B joins after 5 months, which means B invests for 7 months.

### Step 2: Set up the profit-sharing ratio
- The profit is divided in the ratio of 2:3 (A:B).
- This means that A's share of the profit corresponds to 2 parts and B's share corresponds to 3 parts.

### Step 3: Calculate A's contribution in terms of capital and time
- A's contribution can be calculated as:
\[ \text{A's contribution} = \text{Investment} \times \text{Time} = 3500 \times 12 = 42000 \]

### Step 4: Set up the equation for B's contribution
- Let B's contribution be \( X \).
- B invests for 7 months, so B's contribution can be calculated as:
\[ \text{B's contribution} = X \times 7 \]

### Step 5: Set up the ratio equation
- According to the profit-sharing ratio:
\[ \frac{A's contribution}{B's contribution} = \frac{2}{3} \]
- Substitute the contributions into the equation:
\[ \frac{42000}{X \times 7} = \frac{2}{3} \]

### Step 6: Cross-multiply to solve for \( X \)
- Cross-multiplying gives:
\[ 42000 \times 3 = 2 \times (X \times 7) \]
\[ 126000 = 14X \]

### Step 7: Solve for \( X \)
- Divide both sides by 14:
\[ X = \frac{126000}{14} = 9000 \]

### Conclusion
- B's contribution in the capital is Rs. 9000.