Raman and Nakul invested in a business .Raman invested Rs 3000 and withdraw Rs 1500 at the end of `8^(th)` month. Nakul invested Rs 1500 at the end of `7^(th)` month .At the end , they earned Rs 1800. What should be Raman's share ?

Options

A. 1440
B. 920
C. 864
D. 850

Answer

To find Raman's share of the profit, we need to calculate the effective capital contribution of both Raman and Nakul over the time they invested in the business.

### Step 1: Calculate the effective capital contribution for Raman.

Raman invested Rs 3000 for the first 8 months and then withdrew Rs 1500. This means he had Rs 3000 for the first 8 months and Rs 1500 for the last 4 months.

- For the first 8 months:
\[ \text{Capital} = 3000 \times 8 = 24000 \]

- For the last 4 months:
\[ \text{Capital} = 1500 \times 4 = 6000 \]

- Total effective capital contribution for Raman:
\[ \text{Total} = 24000 + 6000 = 30000 \]

### Step 2: Calculate the effective capital contribution for Nakul.

Nakul invested Rs 1500 at the end of the 7th month, which means he invested for only 5 months (from the end of the 7th month to the end of the 12th month).

- For 5 months:
\[ \text{Capital} = 1500 \times 5 = 7500 \]

### Step 3: Calculate the ratio of their contributions.

Now we can find the ratio of their effective capital contributions.

- Raman's contribution: 30000
- Nakul's contribution: 7500

The ratio of Raman's to Nakul's contributions is:
\[ \text{Ratio} = \frac{30000}{7500} = 4:1 \]

### Step 4: Calculate Raman's share of the profit.

The total profit earned is Rs 1800. To find Raman's share, we need to divide the profit in the ratio of their contributions.

- Total parts in the ratio = 4 + 1 = 5 parts.
- Raman's share of the profit:
\[ \text{Raman's share} = \frac{4}{5} \times 1800 = 1440 \]

### Final Answer:
Raman's share of the profit should be Rs 1440.

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