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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] New post 07 Jan 2008, 08:20
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If the circus were to sell all of its 220 tickets for this month's performance at their usual price, the revenue from sales would be 10% greater than that collected last month. However, the circus raised the ticket price by 5% and sold only 200 tickets as a result. What percent less was last month's revenue than that of this month?

A. 2
B. 5
C. 100/21
D. 110/20
E. 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] New post 07 Jan 2008, 08:41
Expert's post
GK_Gmat wrote:
If the circus were to sell all of its 220 tickets for this month's performance at their usual price, the revenue from sales would be 10% greater than that collected last month. However, the circus raised the ticket price by 5% and sold only 200 tickets as a result. What percent less was last month's revenue than that of this month?
2
5
100/21
110/20
9/4


C

Rl - revenue of last month
Rt - revenue of this month at usual prise.
Rt2 - revenue of this month at higher prise.

Rt=220*p=1.1*Rl
Rt2=200*p*1.05=210*p
%=100*(Rt2-Rl)/Rt2=100*(210*p-220/1.1*p)/210*p=100/21
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Re: If the circus were to sell all of its 220 tickets for this [#permalink] New post 07 Jan 2008, 09:48
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Brav-0 Walker! 8-)

Here's my approach:

220p = 1.1RL (220 tickets at regular P price = 1.1 (or 10% more) than revenue last month (RL)
to find RL just multiply each side by 10/11 (1.1*10 = 11/11 = 1)
220(10/11)p = 1.1(10/11)R:
200p = RL (so the revenue last month was = to 200p)

Now what does our revenue look like at the new ticket price this month:

200(1.05)P = 210p

so...if the revenue this month will be 210p, what percentage less was last months revenue at 200p than that of this month?

(210p-200p)/210p = 10p/210p = 1/21
we're looking for percentage though, so multiply this by 100
1/21(100) = 100/21

Answer C
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Re: If the circus were to sell all of its 220 tickets for this [#permalink] New post 07 Jan 2008, 23:02
Thanks guys. You avoided the trap that I fell into, which was calculating final answer as 10/200*100 instead of 10/210*100.
OA is C.
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Re: If the circus were to sell all of its 220 tickets for this [#permalink] New post 07 Jan 2008, 23:17
walker wrote:
GK_Gmat wrote:
If the circus were to sell all of its 220 tickets for this month's performance at their usual price, the revenue from sales would be 10% greater than that collected last month. However, the circus raised the ticket price by 5% and sold only 200 tickets as a result. What percent less was last month's revenue than that of this month?
2
5
100/21
110/20
9/4


C

Rl - revenue of last month
Rt - revenue of this month at usual prise.
Rt2 - revenue of this month at higher prise.

Rt=220*p=1.1*Rl
Rt2=200*p*1.05=210*p
%=100*(Rt2-Rl)/Rt2=100*(210*p-220/1.1*p)/210*p=100/21[/quote

First, I produce the result is only 1/21, and I find no one in the answers matching. When I see this , I got it.

Just an error log, hihi
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Re: If the circus were to sell all of its 220 tickets for this [#permalink] New post 14 Feb 2009, 15:06
walker wrote:
GK_Gmat wrote:
If the circus were to sell all of its 220 tickets for this month's performance at their usual price, the revenue from sales would be 10% greater than that collected last month. However, the circus raised the ticket price by 5% and sold only 200 tickets as a result. What percent less was last month's revenue than that of this month?
2
5
100/21
110/20
9/4


C

Rl - revenue of last month
Rt - revenue of this month at usual prise.
Rt2 - revenue of this month at higher prise.

Rt=220*p=1.1*Rl
Rt2=200*p*1.05=210*p
%=100*(Rt2-Rl)/Rt2=100*(210*p-220/1.1*p)/210*p=100/21


can someone explain why its:
(Rt2-Rl)/Rt2

and not:

(Rt2-Rl)/Rl

I know that the percentage change formula is difference/original, so isn't the original here Rl?
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Re: If the circus were to sell all of its 220 tickets for this [#permalink] New post 14 Feb 2009, 15:16
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GK_Gmat wrote:
... What percent less was last month's revenue than that of this month?


We compare with "that of this month". Therefore, it is a base.

Consider this example:
July revenue = 200
August revenue = 220

What percent more was August revenue than that of July? July is a base. Therefore, (220-200)/200 - it is typical case in our life.
What percent less was July revenue than that of August? August is a base. Therefore, (220-200)/220 - it is reverse case as in the problem.
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Re: If the circus were to sell all of its 220 tickets for this [#permalink] New post 14 Feb 2009, 22:09
Thanks Walker, very well put. I need to memorize this!
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Re: If the circus were to sell all of its 220 tickets for this [#permalink] New post 26 Aug 2010, 22:18
The easiest way to do this is by substituting values .
say Price per ticket = 10
Therefore revenue for 220 tickets =2200
This is 10% higher than last time means last time was 2000
This month they sell 200 tickets for 10.5 ( increase ticket price by 5%)
Therefore revenue this month is 200x 10.5 = 2100

Hence the inrease over last months revenue is 2100-2000=100

% increase= 100 x 100 = 100/21 Ans
******** **** 2100

Last edited by manjot77 on 26 Aug 2010, 22:25, edited 2 times in total.
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Re: If the circus were to sell all of its 220 tickets for this [#permalink] New post 17 Jan 2011, 14:02
manjot77 wrote:
The easiest way to do this is by substituting values .
say Price per ticket = 10
Therefore revenue for 220 tickets =2200
This is 10% higher than last time means last time was 2000
This month they sell 200 tickets for 10.5 ( increase ticket price by 5%)
Therefore revenue this month is 200x 10.5 = 2100

Hence the inrease over last months revenue is 2100-2000=100

% increase= 100 x 100 = 100/21 Ans
******** **** 2100


I like this approach, but could someone please explain the last bit, why do you multiply 100/2100 with 100 ?

many thanks
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Re: If the circus were to sell all of its 220 tickets for this [#permalink] New post 10 Feb 2011, 09:38
hafgola wrote:
manjot77 wrote:
The easiest way to do this is by substituting values .
say Price per ticket = 10
Therefore revenue for 220 tickets =2200
This is 10% higher than last time means last time was 2000
This month they sell 200 tickets for 10.5 ( increase ticket price by 5%)
Therefore revenue this month is 200x 10.5 = 2100

Hence the inrease over last months revenue is 2100-2000=100

% increase= 100 x 100 = 100/21 Ans
******** **** 2100


I like this approach, but could someone please explain the last bit, why do you multiply 100/2100 with 100 ?

many thanks


You're just converting the decimal form into the % form.

100/2100 = 0.0476
or 4.76%
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Re: If the circus were to sell all of its 220 tickets for this [#permalink] New post 08 Jan 2012, 17:11
I missed this one, the wording threw me off of finding which percentage the question was looking for.
Which wording in this question shows that it was this month minus last month divided by this month not last month?
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Re: If the circus were to sell all of its 220 tickets for this [#permalink] New post 06 Jul 2014, 12:42
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Re: If the circus were to sell all of its 220 tickets for this [#permalink] New post 06 Jul 2014, 13:24
Expert's post
GK_Gmat wrote:
If the circus were to sell all of its 220 tickets for this month's performance at their usual price, the revenue from sales would be 10% greater than that collected last month. However, the circus raised the ticket price by 5% and sold only 200 tickets as a result. What percent less was last month's revenue than that of this month?

A. 2
B. 5
C. 100/21
D. 110/20
E. 9/4



For a percentage questions like this one, it's almost always better to plug some smart numbers.

Let the usual price of a ticket be $20 (I chose $20 because $20+5%=$21=integer, which will make calculations easier). This month's revenue for this price would be 220*$20=$4,400 and we are told that it's 10% greater than the revenue collected last month, hence the last month's revenue was $4,400/1.1=$4,000;

Circus raised the ticket price by 5%, so the new price was $21 and the actual revenue from 200 tickets was 200*$21=$4,200;

What percent less would last month's revenue be compared to this month's revenue: percent=\frac{4,200-4,000}{4,200}*100=\frac{100}{21}%. General formula for percent increase or decrease, (percent change): percent=\frac{Change}{Original}*100, so as we are comparing the difference to this month's revenue we should put this value ($4,200) in the denominator.

Answer: C.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-the-circus-were-to-sell-all-of-its-220-tickets-for-this-126466.html
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Re: If the circus were to sell all of its 220 tickets for this   [#permalink] 06 Jul 2014, 13:24
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