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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]

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New post 29 Jul 2010, 13:41
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Difficulty:

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Question Stats:

54% (01:58) correct 46% (02:48) wrong based on 90 sessions

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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
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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]

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New post 29 Jul 2010, 14:42
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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 = \(\frac{10x}{210x}*100 = \frac{100}{21}\)

Answer is C.

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Re: If the circus were to sell all of its 220 tickets for this [#permalink]

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New post 11 Aug 2010, 23:46
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]

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New post 12 Aug 2010, 07:19
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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

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Re: If the circus were to sell all of its 220 tickets for this   [#permalink] 12 Aug 2010, 07:19
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