A starts business with `₹ 7000` and after 5 months. B joins with A as his partner. After 1 year, the profit is dividend in the ratio `2:3`. What is B's contributions in the capital ?

Options

A. `₹13000`
B. `₹ 12000`
C. `₹ 15000`
D. `₹ 18000`

Explanation

To solve the problem, we need to determine B's contribution in the capital based on the information given about the profit sharing ratio and the time each partner invested in the business.

### Step-by-Step Solution:

1. **Identify A's Investment and Time**:
- A starts the business with ₹7000.
- A invests this amount for the entire year (12 months).

2. **Identify B's Investment Time**:
- B joins after 5 months, which means B invests for 7 months (12 months - 5 months).

3. **Set Up the Profit Sharing Ratio**:
- The profit is divided in the ratio of 2:3 (A:B).
- Let B's capital contribution be represented as \( x \).

4. **Calculate A's Contribution in Terms of Capital and Time**:
- A's effective capital contribution can be calculated as:
\[ \text{A's contribution} = \text{Capital} \times \text{Time} = 7000 \times 12 = 84000 \]

5. **Calculate B's Contribution in Terms of Capital and Time**:
- B's effective capital contribution can be calculated as:
\[ \text{B's contribution} = x \times 7 \]

6. **Set Up the Equation Based on Profit Ratio**:
- According to the profit sharing ratio, we can set up the equation:
\[ \frac{A's \ contribution}{B's \ contribution} = \frac{2}{3} \]
- Substituting the values we have:
\[ \frac{84000}{7x} = \frac{2}{3} \]

7. **Cross-Multiply to Solve for x**:
- Cross-multiplying gives:
\[ 3 \times 84000 = 2 \times 7x \]
- This simplifies to:
\[ 252000 = 14x \]

8. **Solve for x**:
- Dividing both sides by 14:
\[ x = \frac{252000}{14} = 18000 \]

9. **Conclusion**:
- B's contribution in the capital is ₹18000.

### Final Answer:
B's contribution in the capital is ₹18000.