A and B invest Rs 60,000 and Rs 80,000 in a business. A receives Rs 100 per month out of Profit for running the business and the rest of the profit is divided in the ratio of investment. If in a year A receives Rs 3,900, what does B receives.

Answer

To solve the problem, we need to determine how much B receives from the profit after A's monthly payment and the profit division based on their investments.

### Step-by-Step Solution:

1. **Calculate A's Total Monthly Payment**:
A receives Rs 100 per month for running the business.
\[ \text{Total payment to A in a year} = 100 \text{ (per month)} \times 12 \text{ (months)} = 1200 \text{ Rs} \]

2. **Calculate A's Total Earnings**:
According to the problem, A receives a total of Rs 3900 in a year.
This total includes both the monthly payment and A's share of the profit.
\[ \text{Total earnings of A} = 3900 \text{ Rs} \]

3. **Calculate A's Share of Profit**:
To find A's share of the profit, we subtract the total monthly payment from A's total earnings.
\[ \text{A's share of profit} = \text{Total earnings of A} - \text{Total payment to A} \]
\[ \text{A's share of profit} = 3900 - 1200 = 2700 \text{ Rs} \]

4. **Determine the Total Investment**:
A's investment = Rs 60,000
B's investment = Rs 80,000
\[ \text{Total investment} = 60000 + 80000 = 140000 \text{ Rs} \]

5. **Calculate the Profit Sharing Ratio**:
The profit is shared in the ratio of their investments.
\[ \text{Ratio of A's investment to B's investment} = 60000 : 80000 = 3 : 4 \]

6. **Calculate Total Parts in the Ratio**:
The total parts in the ratio = 3 + 4 = 7 parts.

7. **Calculate the Value of Each Part**:
Since A's share of profit is Rs 2700, we can find the value of each part.
\[ \text{Value of each part} = \frac{A's share of profit}{\text{A's parts}} = \frac{2700}{3} = 900 \text{ Rs} \]

8. **Calculate B's Share of Profit**:
Now, we can calculate B's share of profit using the value of each part.
\[ \text{B's share of profit} = \text{Value of each part} \times \text{B's parts} = 900 \times 4 = 3600 \text{ Rs} \]

9. **Calculate Total Amount B Receives**:
Finally, we add B's share of profit to any fixed payment (if applicable). In this case, B does not receive a fixed payment like A.
\[ \text{Total amount B receives} = \text{B's share of profit} = 3600 \text{ Rs} \]

### Conclusion:
B receives Rs 3600 from the profit.