A started busines wit Rs. 45,000 and B joned after ward with rs. 30,000. If the profits at the end of one year were divided in the ratio 2:1 respectively, then B would have joined A for business after:

Options

A. 1 months
B. 2 months
C. 3 months
D. 4 months

Answer

To solve the problem, we need to determine when B joined A in the business based on the profit-sharing ratio and the investments made by both A and B.

### Step-by-Step Solution:

1. **Identify the Investments:**
- A started the business with Rs. 45,000.
- B joined later with Rs. 30,000.

2. **Understand the Profit Sharing Ratio:**
- The profits are divided in the ratio of 2:1 (A:B).

3. **Calculate the Time A Worked:**
- A worked for the entire year, which is 12 months.

4. **Let B's Time in the Business be T Months:**
- We need to find the value of T, which represents how long B was in the business.

5. **Set Up the Equation Based on the Profit Sharing Ratio:**
- The profit share can be represented as:
\[ \text{A's share} : \text{B's share} = \frac{A's Investment \times A's Time}{B's Investment \times B's Time} \]
- Plugging in the values:
\[ 2 : 1 = \frac{45,000 \times 12}{30,000 \times T} \]

6. **Cross-Multiply to Solve for T:**
- Cross-multiplying gives:
\[ 2 \times (30,000 \times T) = 1 \times (45,000 \times 12) \]
- Simplifying this:
\[ 60,000T = 540,000 \]

7. **Solve for T:**
- Dividing both sides by 60,000:
\[ T = \frac{540,000}{60,000} = 9 \]
- Therefore, B worked for 9 months.

8. **Determine When B Joined:**
- Since A worked for 12 months and B worked for 9 months, B must have joined A 3 months after A started:
\[ 12 - 9 = 3 \text{ months} \]

### Final Answer:
B would have joined A for business after **3 months**.

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