Ravi starts a business with ₹45000 : After a certain period of time he is joined by Mohan who invests ₹30000. At the end of the year they divide the profit in the ratio 9:4. After how many months did Mohan join Ravi.

Options

A. 4
B. 5
C. 6
D. 2

Answer

To solve the problem step by step, we need to analyze the investments and the profit-sharing ratio between Ravi and Mohan.

### Step 1: Understand the investments
- Ravi starts the business with ₹45,000.
- Mohan joins later with an investment of ₹30,000.

### Step 2: Define the time of investment
- Let’s assume that Mohan invests for \( T \) months.
- Since Ravi invests for the entire year, he invests for 12 months.

### Step 3: Calculate the effective capital contribution
- The profit is divided in the ratio of their effective capital contributions.
- For Ravi, the effective capital contribution is:
\[ \text{Ravi's contribution} = 45000 \times 12 \]
- For Mohan, the effective capital contribution is:
\[ \text{Mohan's contribution} = 30000 \times T \]

### Step 4: Set up the equation based on the profit ratio
- According to the problem, the profit is divided in the ratio of 9:4. This gives us the equation:
\[ \frac{45000 \times 12}{30000 \times T} = \frac{9}{4} \]

### Step 5: Cross-multiply to solve for \( T \)
- Cross-multiplying gives:
\[ 45000 \times 12 \times 4 = 30000 \times T \times 9 \]
- Simplifying this:
\[ 1800000 = 270000 \times T \]
- Dividing both sides by 270000:
\[ T = \frac{1800000}{270000} = \frac{180}{27} = \frac{20}{3} \approx 6.67 \text{ months} \]

### Step 6: Calculate the time Mohan joined
- Since Mohan invested for \( T \) months, and he joined after \( 12 - T \) months:
\[ 12 - T = 12 - \frac{20}{3} = \frac{36}{3} - \frac{20}{3} = \frac{16}{3} \approx 5.33 \text{ months} \]

### Step 7: Finalize the answer
- Since we need the number of months, we can round this to the nearest whole number. Thus, Mohan joined after approximately 5 months.

### Conclusion
Mohan joined Ravi after approximately 5 months.

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