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The question is from CAT Percentages. CAT exam is known to test on basics rather than high funda ideas. 2IIMs CAT question bank provides you with CAT questions that can help you gear for CAT Exam CAT 2023. 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 36?

Question 29: 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 36 tickets, what would be the minimum price (approx) per ticket if the group wanted to buy 36 tickets?

  1. Rs.23,300
  2. Rs.23,250
  3. Rs.23,166.67
  4. Rs.23,500

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Explanatory Answer

Method of solving this CAT Question from Percentages: Which combination would maximize the discount?

There could be 3 possible relevant scenarios:
1) 32 tickets @ 8% discount + 4 tickets (no discount) => Average discount = 8 * \\frac{32}{36}\\) = 7.11
2) 35 tickets @ 7% discount + 1 ticket (no discount) => Average discount = 7 * \\frac{35}{36}\\) = 6.8
3) 24 tickets @ 8% discount + 12 tickets @ 6% discount
=> Average discount = \\frac{(8 * 24) + (6 * 12)}{36}\\) = 7.33
Thus, clearly 3) would give the minimum average ticket price

Now, if 7.33% ticket price is applied, ticket price = 25000– (25000 * 7.33/100) = 23,166.667
But, since the average discount = 7.33%, average ticket price would be lower than 23,166.67.

The question is " what would be the minimum price (approx) per ticket if the group wanted to buy 36 tickets? "
The minimum average ticket price they would need to pay is Rs.23,166.67

Hence, the answer is Rs.23,166.67

Choice B is the correct answer.


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