CAT Practice : Percents, Profits

Foreign Band - High Ticket Prices !! Ring a bell ?

Concert - Ticket Price

Q.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:

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

Choice B. 23,367

Detailed Solution

There could be 3 possible relevant scenarios:

1) 8 tickets @ 8% discount + 5 tickets (no discount) = ) Average discount = $8 * \frac{8}{13} = \frac{64}{13} = 4.9..%$

2) 7 tickets @ 7% discount + 6 tickets (@ 6% discount) = ) Average discount = $8 * \frac{(7 * 7 + 6 * 6)}{13} = \frac{85}{13} = 6.5..%$

3) 12 tickets @ 6% discount + 1 ticket (no discount) = ) Average discount = Certainly less than 6%

So, Scenario 2 is applicable.

Therefore, Average ticket price ≈ $25000 – 25000 * \frac{6.5}{100} = 23,375$. However, the discount is little greater than 6.5%, So,

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.

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