Krishnamurthy started business investing Rs 6000. Three months later Madhavan joined him investing Rs 4000. If they make a profit of Rs 5100 at the end of the year, how much should be Madhavan's share ?

Options

A. Rs 1700
B. Rs 1400
C. Rs 1300
D. Rs 1732.75

Answer

To solve the problem step by step, we will calculate Madhavan's share of the profit based on their investments and the time they invested in the business.

### Step 1: Determine the time of investment for each partner
- Krishnamurthy invested Rs. 6000 for 12 months.
- Madhavan joined 3 months later, so he invested Rs. 4000 for 9 months.

### Step 2: Calculate the capital months for each partner
- For Krishnamurthy:
\[ \text{Capital Months} = \text{Investment} \times \text{Time} = 6000 \times 12 = 72000 \]
- For Madhavan:
\[ \text{Capital Months} = \text{Investment} \times \text{Time} = 4000 \times 9 = 36000 \]

### Step 3: Find the ratio of their investments
- The ratio of their capital months is:
\[ \text{Krishnamurthy : Madhavan} = 72000 : 36000 \]
- Simplifying this ratio:
\[ = 2 : 1 \]

### Step 4: Determine the total profit and the profit share ratio
- The total profit made at the end of the year is Rs. 5100.
- Since the investment ratio is the same as the profit ratio, we can denote:
- Let Krishnamurthy's share of profit be \(2x\)
- Let Madhavan's share of profit be \(x\)

### Step 5: Set up the equation for total profit
- The equation based on their shares is:
\[ 2x + x = 5100 \]
\[ 3x = 5100 \]

### Step 6: Solve for \(x\)
- Dividing both sides by 3:
\[ x = \frac{5100}{3} = 1700 \]

### Step 7: Determine Madhavan's share
- Since Madhavan's share is \(x\):
\[ \text{Madhavan's share} = 1700 \]

### Final Answer
Madhavan's share of the profit is Rs. 1700.

---