Mohan invested Rs. 100,000 in a garment business After few months, Sohan joined him with Rs. 40000. At the end of the year, the total profit was divided between them in ratio 3 : 1 After how many months did Sohan join the business?
A. 3
B. 2
C. 4
D. 5

Options

A. C
B. B
C. A
D. D

Answer

To solve the problem, we will break it down step by step.

### Step 1: Understand the Investments
Mohan invested Rs. 100,000 in the business. After a few months, Sohan joined him with Rs. 40,000. We need to determine how many months after Mohan's initial investment Sohan joined.

### Step 2: Define Variables
Let’s denote the number of months Mohan invested before Sohan joined as \( X \). Therefore, Sohan joined the business after \( X \) months, and he invested for \( 12 - X \) months since the total duration of the business is one year (12 months).

### Step 3: Calculate the Profit Sharing Ratio
The profit is shared in the ratio of their investments multiplied by the time they invested.
- Mohan's investment: Rs. 100,000 for \( 12 \) months.
- Sohan's investment: Rs. 40,000 for \( 12 - X \) months.

### Step 4: Calculate Effective Capital Contribution
Now, we calculate the effective capital contribution for both:
- Mohan's effective capital = \( 100,000 \times 12 = 1,200,000 \)
- Sohan's effective capital = \( 40,000 \times (12 - X) \)

### Step 5: Set Up the Equation Based on Profit Sharing
According to the problem, the profit is divided in the ratio of 3:1. Therefore, we can set up the equation:
\[ \frac{100,000 \times 12}{40,000 \times (12 - X)} = \frac{3}{1} \]

### Step 6: Cross-Multiply to Solve for \( X \)
Cross-multiplying gives us:
\[ 100,000 \times 12 = 3 \times 40,000 \times (12 - X) \]
\[ 1,200,000 = 120,000 \times (12 - X) \]

### Step 7: Simplify the Equation
Dividing both sides by 40,000:
\[ 30 = 3 \times (12 - X) \]
\[ 30 = 36 - 3X \]

### Step 8: Rearrange to Solve for \( X \)
Rearranging gives:
\[ 3X = 36 - 30 \]
\[ 3X = 6 \]
\[ X = 2 \]

### Conclusion
Sohan joined the business after 2 months.

### Final Answer
**Option B: 2 months**