k, l, m together started a business. k invested Rs.6000 for 5 months l invested Rs.3600 for 6 months and m Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of l ?

Options

A. A) Rs. 1640
B. B) Rs. 2500
C. C) Rs. 2160
D. D) Rs. 3000

Answer

To solve the problem step by step, we need to calculate the share of L based on the investments made by K, L, and M.

### Step 1: Calculate the Investment of Each Partner
The investment of each partner is calculated by multiplying the amount invested by the number of months they invested.

- K's investment:
\[ 6000 \text{ (Rs)} \times 5 \text{ (months)} = 30000 \text{ (Rs-months)} \]

- L's investment:
\[ 3600 \text{ (Rs)} \times 6 \text{ (months)} = 21600 \text{ (Rs-months)} \]

- M's investment:
\[ 7500 \text{ (Rs)} \times 3 \text{ (months)} = 22500 \text{ (Rs-months)} \]

### Step 2: Calculate the Total Investment
Now, we sum up the total investment from all three partners.

\[ \text{Total Investment} = 30000 + 21600 + 22500 = 74100 \text{ (Rs-months)} \]

### Step 3: Calculate the Profit Share Ratio
The profit share ratio is based on the investment amounts calculated in Rs-months.

- K's share:
\[ 30000 \]

- L's share:
\[ 21600 \]

- M's share:
\[ 22500 \]

The ratio of their investments is:
\[ K : L : M = 30000 : 21600 : 22500 \]

### Step 4: Simplify the Ratio
To simplify the ratio, we can divide each term by 3000:
\[ K : L : M = 10 : 7.2 : 7.5 \]

To eliminate the decimal, we can multiply each term by 10:
\[ K : L : M = 100 : 72 : 75 \]

### Step 5: Calculate the Total Parts
Now, we find the total parts in the ratio:
\[ \text{Total parts} = 100 + 72 + 75 = 247 \]

### Step 6: Calculate L's Share of the Profit
Now, we can find L's share of the total profit of Rs. 7410. The formula to calculate L's share is:
\[ \text{L's Share} = \left(\frac{\text{L's part}}{\text{Total parts}}\right) \times \text{Total Profit} \]
Substituting the values:
\[ \text{L's Share} = \left(\frac{72}{247}\right) \times 7410 \]

### Step 7: Calculate L's Share
Calculating L's share:
\[ \text{L's Share} = \frac{72 \times 7410}{247} = \frac{532920}{247} \approx 2160 \text{ (Rs)} \]

### Final Answer
Thus, L's share of the profit is Rs. 2160.

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