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CAT 2023 Slot 2 Solved Paper

Instructions [ 40 - 44 ]

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 5‌pm except for Ride3 , for which the last ride has to be completed by 1 pm. Ride gates open every 30 minutes, e.g. 10‌am,10:30‌am, 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.
1. Chitra never waited in the queue and completed her visit by 11 am after spending Rs. 50 to pay for the ticket(s).
2. 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.
3. 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.
4. 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.

Question : 40

Total: 66

What was the total amount spent on tickets (in Rs.) by Bipasha?

Validate

Solution:

Consider Statement 2: Anjali took Ride-1 at 11 am after waiting for 30 minutes for Chitra to complete it. It was the only ride where Anjali waited.
This implies that Chitra took Ride 1 at 10 am. Now we also know that she spent Rs 50 and that she left at 11 am. Now, since she did one ride costing Rs 20 at 10, she must have taken Ride-3 at 9 am.
So we get the following table for Chitra.

	Ride 3	Ride 1
Time	9 am- 10 am	10 am- 11 am
Cost	Rs 30	Rs 20

Now we know that Chitra and Anjali spent Rs 50 before 12:15 pm. It is not possible for Anjali to go on Ride-3 at 10 am as we know that she was waiting for 30 minutes before taking Ride-1 (She was waiting from 10:30 am).
Now, since we know that Ride- 1 was the only ride for which she waited, we can say that she took Ride- 1 at 11 am and started Ride-3 at 12 am
So we get the following table for Anjali.

	Ride-1	Ride-3
Time	11‌am−12‌pm	12‌pm−1‌pm
Cost	20	30

Now, we know that Bipasha started her first ride at 11:30‌am. We also know that they all spent Rs 50 before 12:15 pm.
Therefore, the first ride Bipasha takes will be Ride-2, costing Rs 50 .
So we get the following table for Bipasha.

	Ride-2
Time	11:30 am- 12:30am
Cost	50

We know that Ride 3 stops at 1 pm. So the last ride taken by Anjali will either be Ride- 2 or Ride- 4 . Now, considering Statement 4,we know that the last ride taken by Anjali and Bipasha was same and that Bipasha rode it after Anjali. So their last ride can't be 2.
So the last ride of both Bipasha and Anjali will be 4 .
Now if we assume that immediately after ending Ride-3, Anjali goes to Ride-4, then the last ride of Bipasha will be Ride- 4 from 2 pm - 3 pm. But we know that Bipasha rode 3 rides. So this case is not possible.
Since Anjali didn't have any break or waiting time, the only ride she can ride at 1‌pm will be Ride 2 and then she will go on Ride-4 from 2‌pm to 3‌pm.
So we get the following table for Anjali:

	Ride-1	Ride-3	Ride-2	Ride-4
Time	11‌am=12‌pm	12‌pm−1‌pm	1‌pm=2‌pm	2‌pm=3‌pm
Cost	20	30	50	40

Now we know that the last ride that Bipasha took was Ride- 4 and that she had a gap of 1.5‌hrs before it. This is only possible when she takes one ride between Ride-2 and Ride-4. Since Ride- 3 is closed at 1‌pm, she can only take Ride 1. So we get the following table for her.

	Ride-2	Ride-1	Break	Waiting time	Ride-4
Time	11:30‌am−12:30‌pm	12:30‌pm−1:30‌pm	1:30‌pm−2:30‌pm	2:30‌pm to 3:00‌pm	3‌pm−4‌pm
Cost	50	20			40

As we can see from the table for Bipasha, she spent a total of 50+20+40=110
Therefore the required answer is Option C: 110

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