CAT 2018 Slot 2 — DILR Question 29
Answer the following question based on the information given below.
Each visitor to an amusement park needs to buy a ticket. Tickets can be Platinum, Gold, or Economy. Visitors are classified as Old, Middle-aged, or Young. The following facts are known about visitors and ticket sales on particular day:
- 140 tickets were sold.
- The number of Middle-aged visitors was twice the number of Old visitors, while the number of Young visitors was twice the number of Middle-aged visitors.
- Young visitors bought 38 of the 55 Economy tickets that were sold, and they bought half the total number of Platinum tickets that were sold.
- The number of Gold tickets bought by Old visitors was equal to the number of Economy tickets bought by Old visitors.
If the number of Old visitors buying Platinum tickets was equal to the number of Middle-aged visitors buying Platinum tickets, then which among the following could be the total number of Platinum tickets sold?
Answer & solution
32
- B
34
- C
38
- D
36
From points 1 and 2, the number of tickets bought by Young people = 80, the number of tickets bought by the middle aged people = 40 and the number of tickets bought by the old people = 20.
Using points 3 & 4, we get the following
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Now all the questions can be answered.
We have, 20 - 2y = x + 2y - 20. Therefore, x + 4y = 40.
Therefore, x = 40 - 4y = 4(10 - y)
or 2x = 8(10 - y). Therefore, x is a multiple of 8. Out of the given options, 32 is a possible answer.
Hence, option (a).