In a hotel, the rent of first three days is Rs50 per day and for the next five days, the rent will be Rs100 per day and for the remaining days, the rent will be Rs300 per day. Initially the registration fee is Rs 50. If any guest paid upto Rs1300, then for how many days he stayed in it?

Options

A. 7 days
B. 8 days
C. 9 days
D. 10 days

Answer

To solve the problem, we will break it down into steps:

### Step 1: Calculate the total cost for the first 3 days.
The rent for the first 3 days is Rs. 50 per day.

\[ \text{Cost for first 3 days} = 3 \times 50 = Rs. 150 \]

### Step 2: Add the registration fee.
The registration fee is Rs. 50.

\[ \text{Total cost after 3 days} = \text{Cost for first 3 days} + \text{Registration fee} = 150 + 50 = Rs. 200 \]

### Step 3: Determine the remaining budget.
The total amount paid by the guest is Rs. 1300. We need to find out how much is left after paying for the first 3 days.

\[ \text{Remaining budget} = \text{Total amount paid} - \text{Total cost after 3 days} = 1300 - 200 = Rs. 1100 \]

### Step 4: Calculate the cost for the next 5 days.
The rent for the next 5 days is Rs. 100 per day.

\[ \text{Cost for next 5 days} = 5 \times 100 = Rs. 500 \]

### Step 5: Update the remaining budget after staying for 5 more days.
Now we will subtract the cost for the next 5 days from the remaining budget.

\[ \text{Remaining budget after 8 days} = \text{Remaining budget} - \text{Cost for next 5 days} = 1100 - 500 = Rs. 600 \]

### Step 6: Calculate how many additional days the guest can stay.
The rent for the remaining days is Rs. 300 per day. We will find out how many full days the guest can stay with the remaining budget.

\[ \text{Number of additional days} = \frac{\text{Remaining budget}}{\text{Rent per day for remaining days}} = \frac{600}{300} = 2 \text{ days} \]

### Step 7: Calculate the total number of days stayed.
The total number of days the guest stayed in the hotel is the sum of the first 3 days, the next 5 days, and the additional days.

\[ \text{Total days stayed} = 3 + 5 + 2 = 10 \text{ days} \]

### Final Answer:
The guest stayed for a total of **10 days** in the hotel.

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