# CAT Practice : Percents, Profits

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

## Concert - Ticket Price

Q.29: In the previous question, what would be the minimum price (approx) per ticket if the group wanted to buy 36 tickets?

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

Choice C. 23,166.66

## Detailed Solution

There could be 2 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 = $25000 – 25000 * \frac{7.33}{100} = 23,166.667$. But, since the average discount = 7.33%, average ticket price would be lower than 23,166.67. Therefore,

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