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# If the circus were to sell all of its 220 tickets for this

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If the circus were to sell all of its 220 tickets for this [#permalink]  29 Jul 2010, 12:41
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Difficulty:

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Question Stats:

56% (03:14) correct 44% (02:56) wrong based on 73 sessions
If the circus were to sell all of its 220 tickets for this month's performance at its usual price, the revenue from sales would be 10% greater than that collected last month. If the circus raised the ticket price by 5% and sold only 200 tickets as a result, what percent less would last month's revenue be compared to this month's revenue?

2
5
100/21
110/20
9/4

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-the-circus-were-to-sell-all-of-its-220-tickets-for-this-126466.html
[Reveal] Spoiler: OA

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Re: If the circus were to sell all of its 220 tickets for this [#permalink]  29 Jul 2010, 13:42
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Expert's post
Let us assume that the price per ticket is x for this month. So total revenue = $$220x$$.

$$220x = \frac{110}{100}*A$$ where A is last month's revenue

$$A = \frac{220x*100 }{110} = 200x$$

New price = $$\frac{105}{100}x$$

New revenue by raising price = $$200* \frac{105}{100}x = 210x$$

Difference = 210x - 200x = 10x

Percentage = $$\frac{10x}{210x}*100 = \frac{100}{21}$$

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Re: If the circus were to sell all of its 220 tickets for this [#permalink]  11 Aug 2010, 22:46
This month revenue = 220*x (x BE THE PRICE FOR 1 TICKET)

Last months revenue can be calculated as 220x / 1.10 = 200x
Now consider the next statement - > if the price of ticket is hiked by 5% the new price is 1.05 x.
So the new revenue when only 200 tickets are sold = 200 * 1.05x = 210x.

We need to find the percentage difference ; so we have (new-old/new*100) 210x-200x/210x*100 = 100/21 - Ans C
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Re: If the circus were to sell all of its 220 tickets for this [#permalink]  12 Aug 2010, 06:19
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bogos wrote:
If the circus were to sell all of its 220 tickets for this month's performance at its usual price, the revenue from sales would be 10% greater than that collected last month. If the circus raised the ticket price by 5% and sold only 200 tickets as a result, what percent less would last month's revenue be compared to this month's revenue?

2
5
100/21
110/20
9/4

Good solutions so far, but seriously... I personally find them much too time consuming (I hate writing down fractions and whenever I can prevent working with unkowns I do... --> lazy )

So my simple and fast approach:

1st: Let this month's ticket price = 1
2nd: Calculate this month's revenue = 220 x 1 = 220
3rd: This month is 10% more than last month, hence last month revenue was 200
4th: Increase the ticket price 5% to 1.05
5th: Calculate new revenue with increased price: 1.05x200 = 210
6th: Compare 210 to 200 --> 210 is 5% more than 200, so locially, 200 is some number a little less than 5% smaller than 210 --> only solution: C

Cheers,
André
Re: If the circus were to sell all of its 220 tickets for this   [#permalink] 12 Aug 2010, 06:19
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# If the circus were to sell all of its 220 tickets for this

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