A started a business by investing Rs. 36,000. After 4 month B joined him with some investment. At the end of the year, the total profit was divided between them in the ratio of 9 : 7 how much capital was invested by B in the business?

Answer

To solve the problem, we need to determine how much capital B invested in the business, given the profit-sharing ratio and the time of investment for both A and B.

### Step-by-Step Solution:

1. **Identify A's Investment and Time:**
- A invested Rs. 36,000.
- A invested this amount for the entire year (12 months).

**Calculation:**
\[ \text{A's investment contribution} = 36,000 \times 12 = 432,000 \]

2. **Determine B's Time of Investment:**
- B joined A after 4 months, meaning B invested for the remaining 8 months of the year.

**Calculation:**
\[ \text{B's time of investment} = 12 - 4 = 8 \text{ months} \]

3. **Set Up the Profit Sharing Ratio:**
- The total profit is shared in the ratio of 9:7 (A:B).
- Let A's contribution be represented as \(9x\) and B's contribution as \(7x\).

4. **Express B's Investment in Terms of x:**
- From the profit-sharing ratio, we know:
\[ \frac{\text{A's investment contribution}}{\text{B's investment contribution}} = \frac{9}{7} \]
- We can express this as:
\[ \frac{432,000}{\text{B's contribution} \times 8} = \frac{9}{7} \]

5. **Cross Multiply to Solve for B's Contribution:**
- Let B's contribution be \(B\).
\[ 432,000 \times 7 = 9 \times (B \times 8) \]
- Simplifying gives:
\[ 3024,000 = 72B \]

6. **Calculate B's Investment:**
- Divide both sides by 72 to find B's investment:
\[ B = \frac{3024,000}{72} = 42,000 \]

### Final Answer:
B invested Rs. 42,000 in the business.