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The question is from CAT Percentages. 2IIMs CAT question bank provides you with CAT questions that can help you gear for CAT Exam CAT 2019. Percentages is an important topic for CAT. A band is giving group discounts based on the number of tickets. What could be the optimum price for a group of 13? Foreign Band - High Ticket Prices !! Ring a bell ?

Question 28: Recently a band was to perform in India. However, there was widespread criticism of the high cost of its tickets so the organizers decided to offer the following discounts:
CAT : Arithmetic: Percents; Profits - Group discount
The tickets were originally priced at Rs 25,000/ticket. Any additional tickets (above the lot sizes) were billed at the original price.A college group wants to buy 13 tickets, what is the minimum average ticket price they would need to pay (approx.)?

  1. 23,375
  2. 23,367
  3. 23,380
  4. 23,400

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Explanatory Answer

Method of solving this CAT Question from Percentages: Which combination would minimize the ticket price?

There could be 3 possible relevant scenarios:
1) 8 tickets @ 8% discount + 5 tickets (no discount) => Average discount = 8 * 8/13 = 64/13 = 4.9..
2) 7 tickets @ 7% discount + 6 tickets (@ 6% discount) => Average discount = (7*7+6*6)/13 = 85/13 = 6.5..
3) 12 tickets @ 6% discount + 1 ticket (no discount) => Average discount = Certainly less than 6%
So, Scenario 2 is applicable.
Therefore, Average ticket price ≈ 25000–25000 * 6.5/100 = 23,375.
However, the discount is little greater than 6.5%, So, the answer is 23,367.
Note – Be careful when the options are given as close as in this question. Don’t ignore the decimal points of percentages in such cases.

The question is "what is the minimum average ticket price they would need to pay (approx.)?"
The minimum average ticket price they would need to pay is Rs.23,367

Hence, the answer is 23,367.

Choice B is the correct answer.


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