Entry fee is Re. 1. There are 3 rides, each costing Re. 1. A total of 3000…
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Entry fee is Re. 1. There are 3 rides, each costing Re. 1. A total of 3000 students enter. Total income is Rs. 7200. 800 students go on all 3 rides. 1400 students go on at least 2 rides. No student repeats the same ride. How many students do not go on any ride?
- A.
600
- B.
900
- C.
1000
- D.
1100
Attempted by 6 students.
Show answer & explanation
Correct answer: C
This is a part-whole word problem: the total number of students splits into disjoint groups by how many rides each took, and the total income splits into a fixed part (entry fees, paid by every student) plus a variable part (ride fees, paid per ride). Subtracting the fixed part isolates the total number of rides taken, which can be distributed across the known rider-groups to solve for any missing group size.
Entry fee income = 3000 students × Re. 1 = Rs. 3000.
Ride income = Total income − Entry income = 7200 − 3000 = Rs. 4200, which equals the total number of rides taken (since each ride costs Re. 1).
Students who took all 3 rides = 800, so rides consumed by them = 800 × 3 = 2400.
Students who took at least 2 rides = 1400, so students who took exactly 2 rides = 1400 − 800 = 600, and rides consumed by them = 600 × 2 = 1200.
Rides accounted for so far = 2400 + 1200 = 3600. Remaining rides = 4200 − 3600 = 600; since no student repeats a ride, these belong to 600 different students who took exactly 1 ride.
Students who went on at least one ride = 800 + 600 + 600 = 2000.
Students who went on no ride = 3000 − 2000 = 1000.
Check: total income = entry income + ride income = 3000 + (2400 + 1200 + 600) = 3000 + 4200 = 7200, matching the given total; and the four groups 800 + 600 + 600 + 1000 = 3000, matching the total student count.
So 1000 students did not go on any ride.