CAT 2023 Slot 2 — DILR Question 6
Answer the following questions based on the information given below:
Anjali, Bipasha, and Chitra visited an entertainment park that has four rides. Each ride lasts one hour and can accommodate one visitor at one point. All rides begin at 9 am and must be completed by 5 pm except for Ride-3, for which the last ride has to be completed by 1 pm. Ride gates open every 30 minutes, e.g. 10 am, 10:30 am, and so on. Whenever a ride gate opens, and there is no visitor inside, the first visitor waiting in the queue buys the ticket just before taking the ride. The ticket prices are Rs. 20, Rs. 50, Rs. 30 and Rs. 40 for Rides 1 to 4, respectively. Each of the three visitors took at least one ride and did not necessarily take all rides. None of them took the same ride more than once. The movement time from one ride to another is negligible, and a visitor leaves the ride immediately after the completion of the ride. No one takes a break inside the park unless mentioned explicitly.
The following information is also known.
- Chitra never waited in the queue and completed her visit by 11 am after spending Rs. 50 to pay for the ticket(s).
- Anjali took Ride-1 at 11 am after waiting for 30 mins for Chitra to complete it. It was the only ride where Anjali waited.
- Bipasha began her first of three rides at 11:30 am. All three visitors incurred the same amount of ticket expense by 12:15 pm.
- The last ride taken by Anjali and Bipasha was the same, where Bipasha waited 30 mins for Anjali to complete her ride. Before standing in the queue for that ride, Bipasha took a 1-hour coffee break after completing her previous ride.
What was the total amount spent on tickets (in Rs.) by Bipasha?
Answer & solution
110
- B
100
- C
90
- D
120
Easy
The whole set hinges on building one master timetable. Anchor it with Chitra (no waiting, finished early), then slot in Anjali, then Bipasha. The "same expense of Rs. 50 by 12:15 pm" clue is the master key — it pins down exactly which rides each person bought by then. The same schedule answers all five questions.
Ride lengths hour. Ticket prices: . Ride-3's last slot must finish by 1 pm. Solving the clues gives this master timetable:
Chitra (Fact 1). She never waited, finished by 11 am, and spent exactly Rs. 50. With no waiting she rides back-to-back from 9 am, so at most two rides (9–10, 10–11). The only way to total from distinct rides without R2-alone (R2 would block Fact 2) is . Fact 2 needs Chitra on R1 until 11 am, so she rides R3 (9–10) then R1 (10–11).
Anjali (Fact 2). She reaches R1's gate at 10:30, but Chitra is inside until 11 am, so Anjali waits 30 min and takes R1 (11–12) — her only wait of the day.
The Rs. 50 lock (Fact 3). By 12:15 pm all three have spent the same amount. Chitra spent , so Anjali and Bipasha must also have spent exactly by 12:15.
Anjali has paid for R1; she needs by 12:15, i.e. R3 (12–1) (and R3 is legally completed by 1 pm). So Anjali R1, R3 so far.
Bipasha's first ride (Fact 3). Her first of three rides starts at 11:30. To reach exactly by 12:15 from a single ride begun at 11:30, that ride must be R2 (11:30–12:30), costing .
The shared last ride (Fact 4). Anjali and Bipasha end on the same ride, with Bipasha waiting 30 min for Anjali, after a 1-hr coffee break. After R1, R3, Anjali takes R2 (1–2), then her final R4 (2–3). Bipasha, after R2, takes R1 (12:30–1:30), then a coffee break (1:30–2:30), then queues for R4 — waits while Anjali rides (2:30–3) and takes R4 (3–4).
Master timetable:
| Visitor | Rides (in order) | Tickets paid |
|---|---|---|
| Chitra | R3 (9–10), R1 (10–11) | |
| Anjali | R1 (11–12), R3 (12–1), R2 (1–2), R4 (2–3) | |
| Bipasha | R2 (11:30–12:30), R1 (12:30–1:30), R4 (3–4) |
This question. Bipasha took R1, R2 and R4, so her ticket total is .