In a hotel the average expenditure per guest is Rs 60 when there are 10 guests and the average expenditure per guest is Rs 40 when there are 20 guests. Assume that there are some fixed expenses which do not depend on the number of guests and the remaining expenses vary directly with the number of guests. What will be the average expenditure per guest when there are 40 guests in the hotel?

Introduction:
This question studies the effect of fixed and variable expenses on the average cost per guest in a hotel. Some costs remain the same regardless of the number of guests, while others change in direct proportion to the number of guests. By using two given scenarios we can find the fixed and variable parts and then predict the average for a different number of guests.

Given Data / Assumptions:
- When there are 10 guests, average expenditure per guest = Rs 60. - When there are 20 guests, average expenditure per guest = Rs 40. - There is a fixed expense F that does not depend on the number of guests. - There is a variable expense per guest v, so variable total expense is v times number of guests. - We must find the average expenditure per guest when there are 40 guests.

Concept / Approach:
Total expenditure for a given number of guests = fixed expense + variable expense per guest times number of guests. Average expenditure per guest = total expenditure divided by number of guests. Using the two given average values for 10 and 20 guests we set up two equations in F and v. Solving these equations gives F and v, which can then be used to compute the average for 40 guests.

Step-by-Step Solution:
Step 1: Let F be the fixed expense and v be the variable expense per guest. Step 2: For 10 guests, total expenditure = F + 10v. Step 3: Average for 10 guests is 60, so (F + 10v) / 10 = 60, giving F + 10v = 600. Step 4: For 20 guests, total expenditure = F + 20v. Step 5: Average for 20 guests is 40, so (F + 20v) / 20 = 40, giving F + 20v = 800. Step 6: Subtract the equation in Step 3 from the equation in Step 5 to eliminate F. Step 7: (F + 20v) - (F + 10v) = 800 - 600 gives 10v = 200. Step 8: Solve for v: v = 200 / 10 = 20. Step 9: Substitute v = 20 into F + 10v = 600 to find F. Step 10: F + 10 * 20 = 600 gives F + 200 = 600, so F = 400. Step 11: For 40 guests, total expenditure = F + 40v = 400 + 40 * 20 = 400 + 800 = 1200. Step 12: Average expenditure per guest for 40 guests = 1200 / 40 = 30.

Verification / Alternative Check:
We can check consistency. With F = 400 and v = 20, for 10 guests total = 400 + 10 * 20 = 600; average = 600 / 10 = 60, which matches the given data. For 20 guests total = 400 + 20 * 20 = 800; average = 800 / 20 = 40, again matching. Thus the model is correct and the predicted average for 40 guests is reliable.

Why Other Options Are Wrong:
Options Rs 25 and Rs 20 would correspond to lower variable expenses or different fixed expenses that do not fit the given data. Option Rs 35 and Rs 40 are too high and ignore the trend that average cost per guest decreases as the number of guests increases due to fixed costs being spread over more people.

Common Pitfalls:
Some students attempt to average 60 and 40 directly or assume a linear change in average without considering the role of fixed expenses. The correct method is to express the total expenditure algebraically, separate the fixed and variable parts and solve systematically using the given averages.

Final Answer:
The average expenditure per guest when there are 40 guests is Rs 30.