An amusement park charges an entry fee of Re. 1 and Re. 1 for each of three…
2025
An amusement park charges an entry fee of Re. 1 and Re. 1 for each of three rides. A total of 3,000 boys enter, and the total revenue is Rs. 7,200. Of them, 800 take all three rides and 1,400 take at least two rides. No boy takes the same ride more than once. How many boys do not take any ride?
Answer: C. 1000 — ConceptSeparate the fixed entry-fee revenue from the ride-fee revenue. Because each ride costs Re. 1, the remaining revenue equals the total number of ride…
- A.
600
- B.
900
- C.
1000
- D.
1100
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Show answer & explanation
Correct answer: C
Concept
Separate the fixed entry-fee revenue from the ride-fee revenue. Because each ride costs Re. 1, the remaining revenue equals the total number of ride uses.
Partition the visitors into those taking exactly one, exactly two, and exactly three rides. The number taking at least two rides includes both the exactly-two and exactly-three groups.
Application
Entry-fee revenue = 3,000 × Re. 1 = Rs. 3,000.
Ride-fee revenue = Rs. 7,200 − Rs. 3,000 = Rs. 4,200, so there are 4,200 ride uses.
Exactly-two riders = 1,400 − 800 = 600, because the 1,400 at-least-two riders include the 800 exactly-three riders.
Ride uses by the exactly-three group = 800 × 3 = 2,400; ride uses by the exactly-two group = 600 × 2 = 1,200.
Ride uses left for exactly-one riders = 4,200 − 2,400 − 1,200 = 600, so 600 boys take exactly one ride.
Boys taking at least one ride = 800 + 600 + 600 = 2,000. Therefore, boys taking no ride = 3,000 − 2,000 = 1,000.
Cross-check
The rider groups account for 600 × 1 + 600 × 2 + 800 × 3 = 4,200 ride uses, exactly matching the ride-fee revenue. Thus the required number is 1,000.