Visitors to show were charged Rs.15 each on the first day. Rs.7.50 on the…
2023
Visitors to show were charged Rs.15 each on the first day. Rs.7.50 on the second day, Rs.2.50 on the third day and total attendance on the three days were in ratio 2:5:13 respectively. The average charge per person for the whole show is?
- A.
Rs. 3.00
- B.
Rs. 4.50
- C.
Rs. 5.00
- D.
Rs. 7.50
Attempted by 5 students.
Show answer & explanation
Correct answer: C
Concept: When a rate (here, the ticket charge) differs across groups of different sizes, the overall average is not the plain mean of the rates. It is the weighted average — the sum of (rate × group size) divided by the sum of the group sizes — with each group's attendance share acting as its weight.
Day | Charge (Rs.) | Attendance ratio |
|---|---|---|
Day 1 | 15.00 | 2 |
Day 2 | 7.50 | 5 |
Day 3 | 2.50 | 13 |
Take the attendance ratio parts as the weights: 2, 5, and 13, which together total 2 + 5 + 13 = 20 parts.
Multiply each day's charge by its own weight: 15 × 2 = 30, 7.50 × 5 = 37.50, and 2.50 × 13 = 32.50.
Add the three products to get the total weighted charge collected: 30 + 37.50 + 32.50 = 100.
Divide this total by the total number of parts to get the average charge per visitor: 100 ÷ 20 = 5.00.
Cross-check: Scale the ratio to real attendance numbers, say 20, 50, and 130 visitors (each part × 10). Total collection = 15 × 20 + 7.50 × 50 + 2.50 × 130 = 300 + 375 + 325 = 1000, and total visitors = 20 + 50 + 130 = 200, so average = 1000 ÷ 200 = 5.00 — the same figure, confirming the result holds regardless of the actual scale of attendance.
So the average charge per person for the whole show is Rs. 5.00.