The average expenditure of the hotel when there are 10 guests is Rs. 80 per guests and the average expenditure is Rs.40 when there are 30 Guests. If it is known that there are some fixed expenses irrespective of the number of guests then the average expenditure per guest when there are 50 guests in the hotel.?a)Rs. 25b)Rs. 32c)Rs. 50d)Rs. 45e)None of theseCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Let the fixed expenditure of the hotel be Rs.x and the variable expenditure is Rs.y , then
x + 10y = 800 ---------(1)
x + 30y = 1200 ----------(2)
20y = 400
y = Rs. 20 and x= 600
Hence the total expenditure when there are 50 guests = 600 + 50 x 20

= 1600
Average expenditure = 1600 /50

= Rs. 32

Answer

Let's solve this problem step by step:

Step 1: Calculate the total expenditure when there are 10 guests.
According to the given information, the average expenditure when there are 10 guests is Rs. 80 per guest. Therefore, the total expenditure for 10 guests will be 10 * 80 = Rs. 800.

Step 2: Calculate the total expenditure when there are 30 guests.
Similarly, the average expenditure when there are 30 guests is Rs. 40 per guest. Therefore, the total expenditure for 30 guests will be 30 * 40 = Rs. 1200.

Step 3: Calculate the difference in total expenditure.
The difference in total expenditure is Rs. 1200 - Rs. 800 = Rs. 400.

Step 4: Calculate the fixed expenses.
Since the difference in total expenditure is due to fixed expenses, we can calculate the fixed expenses by dividing the difference by the number of guests. In this case, the fixed expenses will be Rs. 400 / 20 = Rs. 20 per guest.

Step 5: Calculate the average expenditure when there are 50 guests.
Now, we can calculate the average expenditure when there are 50 guests. The total expenditure for 50 guests will be 50 * (average expenditure per guest) = 50 * (40 + fixed expenses) = 50 * (40 + 20) = 50 * 60 = Rs. 3000.
Therefore, the average expenditure per guest when there are 50 guests is Rs. 3000 / 50 = Rs. 60.

So, the correct answer is not available in the given options, none of these.

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