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M25 #33

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M25 #33 [#permalink] New post 02 May 2009, 17:35
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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

(A) 2
(B) 5
(C) \frac{100}{21}
(D) \frac{110}{20}
(E) \frac{9}{4}

[Reveal] Spoiler: OA
C

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I dont understand what i am doing incorrectly, please help:

What i did is : I took Price for this month as 10$. Which gives me profit for this month -> 2200= 220*10, and profit for last month $2000 (since this month profit is 10% greater than last month profit. If the price is increased by 5% and the tickets sold are 200 than we have a profit of $2100=200*(10*1.05). Than the profit will be less by 5% -> 100/2000=0.05. No? Can you please explain to me what I'm doing incorrectly?
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Re: M25 #33 [#permalink] New post 03 May 2009, 13:30
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I got 5% initially as well. But looking at the OA, I think it's a matter of misinterpreting the wording.

5% would be the percent less compare to last month's revenue (since 2000 is use for the denominator).
100/21 would be percent less compare to this month's revenue (100/2100*100%).

That's just my two cents
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Re: M25 #33 [#permalink] New post 04 May 2009, 06:24
Thank you! :-D
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Re: M25 #33 [#permalink] New post 06 May 2009, 17:15
"what percent less would last month's revenue be compared to this month's revenue", yeah here's the trick.
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Re: M25 #33 [#permalink] New post 14 Sep 2010, 04:07
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Let last month revenue be 100
Therefore, this month revenue is (110/100) * 100 = 110
Usual ticket price is 110/220 = 1/2
Raised ticket price is (105/100) * (1/2) = 105/200
Total revenue after price raise is (105/200) * 200 = 105
Difference in revenue is 105-100 = 5
% difference is (5/105)*100 = 100/21
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Re: M25 #33 [#permalink] New post 14 Sep 2010, 05:37
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Going the algebra way,

Let the price of a ticket be x.
Since the ticket is sold at a usual price in both months, the tickets sold last month are 10% less than the tickets sold this month.

Hence last month's revenue is -> 200x

Since this month, the price of ticket is 5% more than last year's price. Hence, this month's revenue is -> 200 * 1.05 * x = 210x

Difference in revenue is 10x.
Therefore, Percentage Difference in Revenue (With respect to this month's revenue) is ->

(10x/210x) * 100

=100/21 (Answer)

@kt00381n:
By the way, as asimov said, it was just the wording that confused you. Your calculations are correct. Just that the last calculation shall be '100/2100' instead of '100/2000'.

Happiness!
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Re: M25 #33 [#permalink] New post 14 Sep 2010, 08:23
thanks for the explanations... gud question on percents...
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Re: M25 #33 [#permalink] New post 14 Sep 2010, 09:36
Percentage decrease is

(new - old) / (old)

So why isnt it

(this month - last month) / (last month)?
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Re: M25 #33 [#permalink] New post 14 Sep 2010, 10:37
numerator in ur formula is correct. denominator will be based on the basis of comparison. here the basis of comparison is this month's revenue (" compared to this month’s revenue"- last few words in the question states this)

hope it is clear now.
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Re: M25 #33 [#permalink] New post 14 Sep 2010, 12:42
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ksharma12 wrote:
Percentage decrease is

(new - old) / (old)

So why isnt it

(this month - last month) / (last month)?



That is because in the question it is specifically mentioned in the last line that - "what percent less would last month’s revenue be compared to this month’s revenue", that is why are using \frac{\text{Difference}}{\text{This Month}}.
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Re: M25 #33 [#permalink] New post 14 Sep 2010, 18:11
Revenue last month is 10% less than "potential revenue selling 220 tickets at usual price". Usual price means no price change compared to previous month. Hence 200 tickets were sold last month (10% less than 220).
We can assume the total revenue of last month to be 200x (where x is the usual price). Let's x be 1. Hence 200 in revenue last month.

Now this month the ticket price is raised by 5% and 200 are sold, hence 210 in revenue.

Last month revenue is that much less of this month's revenue: (210-200)/210*100%=10/210*100%=100/21%
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Re: M25 #33 [#permalink] New post 15 Sep 2010, 18:58
wording is the tricky part of the question.
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Re: M25 #33 [#permalink] New post 16 Sep 2011, 06:12
C 100/21. But I agree with the wording being tricky. I had to reread the question
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Re: M25 #33 [#permalink] New post 16 Sep 2011, 12:45
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%dec = (New-old)/New = (105-100)/105 *100 = 100/21
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Re: M25 #33 [#permalink] New post 27 Mar 2012, 01:36
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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?

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 (choose $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}%.

Answer: C.
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Re: M25 #33 [#permalink] New post 26 May 2012, 10:51
shreychakravortyi used the algebraic method as well. However i screwed with calculating the percentage change. however, now i see that i must consciously tyr and use the picking no. strategy more often. Tend to rely too heavily on algebra.
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Re: M25 #33 [#permalink] New post 18 Sep 2012, 05:09
You might find it useful to use a bit of SC strategy here. What is being compared? This month's revenue. The compared item is always the denominator.

B.
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Re: M25 #33 [#permalink] New post 19 Sep 2012, 20:13
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Suppose Last month's Price = 100
If increase price by 5% =105
then sold 200 tickets i.e = 200 * 105 = 21000
if sold all 220 tickets for same 100 = 20000

so difference in revenue will be (21000 -20000)/21000 * 100

i.e 1 /21 *100 which is 100 /21.

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Re: M25 #33 [#permalink] New post 17 Sep 2013, 13:36
Another algebraic way....which might help a few

P is usual price
TLM is Total last month
TTM is Total this month

220*P=TLM*1.1
200*P*1.05 = TTM

=> ratio of TLM to TTM is 1.05

Now we want,
(TLM - TTM)/TTM
=(1-1.05)/1.05---using the above ratio
=1/21

we want it in percent terms => (100/21)%

I Hope it helps..!
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Re: M25 #33 [#permalink] New post 19 Sep 2013, 11:13
I have answer C.

I took price ticket equals 100 and then just did the maths
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