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circus tickets

by mehrasa » Fri Sep 16, 2011 11:02 pm
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

to me the answer is B, what do you think?
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by cans » Fri Sep 16, 2011 11:17 pm
price=p. 220p = 1.1m (m is last month's revenue)
p=m/200
(200)(1.05p) = 210p = 210m/200 = 1.05m
this month revenue=1.05m and last month's=m
% less = .05m/1.05m * 100% = 100/21 *
IMO C
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by mehrasa » Sat Sep 17, 2011 12:40 am
the Q is saying what percent less.. at first, I also thought this should be a fraction of last month's revenue and that of this month... to me, because we found 0.95 then this month revenue is %5 less so the answer will be B..
any another idea?
Last edited by mehrasa on Sat Sep 17, 2011 12:44 am, edited 1 time in total.
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by knight247 » Sat Sep 17, 2011 12:42 am
For last month
Revenue=R
Ticket Price=x
Number of tickets sold=N1
R=x*N1

Then we have a tentative scenario as described in the 1st line of the problem
Number of tickets sold=N2=220
Ticket price is still x
Revenue=R+10R/100=1.1R
1.1R=x*220

R=x*220/1.1
R=200x

Comparing this with statement 1 we get N1=200

Third Scenario is
Price per ticket=x+x5/100=1.05x
Number of tickets sold=200
Final Revenue=F=1.05x*200
F=210x

Now, %decrease=(210x-200x)*100/210x=100/21 Hence C. How did you get 5? can you show your work
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by mehrasa » Sat Sep 17, 2011 12:48 am
ok.. i got it.. actually I calculated this month's ticket price with %5 decrease instead of increase and found this month's revenue 0.95 last month then i concluded this is 5% decline compared to the last month.
thnx cans and Knight :)
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