Subodh started a business, investing Rs. 45000. After 4 months. Nepal joined him investing Rs. 30000. If the total profit earned by them at the end of the year was Rs. 13,000 what would be the difference between the shares of Subodh and Nepal ?

Options

A. Rs 7000
B. Rs 3000
C. Rs 9000
D. None of these

Answer

To find the difference between the shares of Subodh and Nepal in the business, we will follow these steps:

### Step 1: Calculate the effective investment of Subodh and Nepal
Subodh invested Rs. 45,000 for 12 months (1 year), while Nepal invested Rs. 30,000 for 8 months (since he joined after 4 months).

- Subodh's investment in terms of months:
\[ 45000 \times 12 = 540000 \]

- Nepal's investment in terms of months:
\[ 30000 \times 8 = 240000 \]

### Step 2: Find the ratio of their investments
Now we can find the ratio of their investments:

\[ \text{Ratio of Subodh to Nepal} = 540000 : 240000 \]

To simplify this ratio, we can divide both sides by 60000:

\[ \frac{540000}{60000} : \frac{240000}{60000} = 9 : 4 \]

### Step 3: Calculate the total profit and their shares
The total profit earned by Subodh and Nepal at the end of the year is Rs. 13,000.

- Total parts in the ratio = 9 + 4 = 13

Now, we can find each person's share of the profit:

- Subodh's share:
\[ \text{Subodh's share} = \frac{9}{13} \times 13000 = 9000 \]

- Nepal's share:
\[ \text{Nepal's share} = \frac{4}{13} \times 13000 = 4000 \]

### Step 4: Find the difference between their shares
Now we can find the difference between Subodh's and Nepal's shares:

\[ \text{Difference} = 9000 - 4000 = 5000 \]

### Final Answer
The difference between the shares of Subodh and Nepal is Rs. 5,000.

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