The rent of a guest house for first 3 days is 50 per day, for next 5 days is 100 per day and for further days is 300 per day. Initial registration Fee is 50. If a guest paid 300 in total then for how many days he stayed in guest house?

Options

A. 4
B. 7
C. 8
D. 10

Answer

To solve the problem step by step, we will break down the costs associated with the guest house stay and determine how many days the guest stayed based on the total payment made.

### Step-by-Step Solution:

1. **Identify the Costs:**
- For the first 3 days, the rent is ₹50 per day.
- For the next 5 days, the rent is ₹100 per day.
- For any further days, the rent is ₹300 per day.
- There is also an initial registration fee of ₹50.

2. **Calculate the Total Rent for the First 3 Days:**
\[ \text{Total Rent for first 3 days} = 3 \times 50 = ₹150 \]

3. **Calculate the Total Rent for the Next 5 Days:**
\[ \text{Total Rent for next 5 days} = 5 \times 100 = ₹500 \]

4. **Calculate the Total Payment Made by the Guest:**
- The guest paid a total of ₹300, which includes the registration fee.
- Therefore, we need to subtract the registration fee from the total payment to find out how much was spent on rent:
\[ \text{Total Rent Paid} = \text{Total Payment} - \text{Registration Fee} = 300 - 50 = ₹250 \]

5. **Determine How Many Days the Guest Stayed:**
- The total rent for the first 3 days is ₹150. Since the guest paid ₹250 for rent, we can see that they stayed beyond the first 3 days.
- Calculate the remaining rent after the first 3 days:
\[ \text{Remaining Rent} = 250 - 150 = ₹100 \]
- The remaining rent of ₹100 corresponds to the next 5 days where the rent is ₹100 per day. Thus, the guest stayed for 1 additional day at this rate.

6. **Calculate the Total Number of Days Stayed:**
- The guest stayed for the first 3 days plus the additional 1 day:
\[ \text{Total Days Stayed} = 3 + 1 = 4 \text{ days} \]

### Final Answer:
The guest stayed for a total of **4 days** in the guest house.

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