Visitors to a show are charged Rs 15 per person on the first day, Rs 7.50 per person on the second day and Rs 2.50 per person on the third day. The attendance on these three days is in the ratio 2 : 5 : 13 respectively. What is the average charge per visitor over the entire three day period?

Introduction / Context:
This problem is an application of weighted averages. The ticket prices differ on three different days, and the number of visitors also differs each day. We are asked to calculate the overall average charge per visitor for the entire three day show. Since the attendance is not the same every day, a simple arithmetic mean of the three prices would be incorrect. Instead, we must weight each price by the corresponding attendance ratio.

Given Data / Assumptions:
- Ticket price on day one is Rs 15 per visitor.
- Ticket price on day two is Rs 7.50 per visitor.
- Ticket price on day three is Rs 2.50 per visitor.
- Attendance ratio for the three days is 2 : 5 : 13.
- We need the overall average ticket charge per person for all three days combined.

Concept / Approach:
To compute the weighted average price, assume a convenient total attendance that respects the given ratio. For example, let the number of visitors on day one be 2x, on day two be 5x and on day three be 13x. Then compute the total revenue from each day (price multiplied by visitors for that day). Add the revenues to get total revenue and add the visitors to get total number of persons. The average price is then total revenue divided by total attendance. The factor x cancels out in the ratio calculation.

Step-by-Step Solution:
Step 1: Let attendance on day one = 2 units, day two = 5 units, day three = 13 units. Step 2: Revenue from day one = 2 * Rs 15 = Rs 30. Step 3: Revenue from day two = 5 * Rs 7.50 = Rs 37.50. Step 4: Revenue from day three = 13 * Rs 2.50 = Rs 32.50. Step 5: Total revenue for three days = 30 + 37.50 + 32.50 = Rs 100. Step 6: Total attendance = 2 + 5 + 13 = 20 units. Step 7: Average charge per visitor = total revenue / total attendance = 100 / 20 = Rs 5.

Verification / Alternative check:
We can verify this by choosing an actual number of visitors, for example multiply each attendance unit by 10 so that day one has 20 visitors, day two has 50 visitors and day three has 130 visitors. Compute revenue with these numbers and divide by total visitors. The revenue values will scale by 10, as will total visitors, and the average will still be Rs 5. This confirms that using ratio units was sufficient and correct.

Why Other Options Are Wrong:
Rs 5.50, Rs 6 and Rs 7 all exceed the computed weighted average of Rs 5. Simply averaging the three ticket prices (15, 7.50 and 2.50) would give (15 + 7.50 + 2.50)/3 = 25/3 which is about 8.33, but that ignores the attendance differences and clearly does not match any option. Only Rs 5 reflects the correct total revenue divided by the correct total number of visitors based on the attendance ratio.

Common Pitfalls:
A very common mistake is to average the three prices directly without accounting for the number of visitors each day. Another pitfall is mixing up the ratio of attendance and mistakenly treating it as money distribution rather than head count. Precise multiplication of price and attendance units before summing ensures the correct weighted average is obtained.

Final Answer:
The overall average charge per visitor over the three days is Rs 5.