Please help me to find an easy way to solve this PS

Question

If the circus were to sell 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

GMATGuruNY · Answer

ranjani2002 wrote:If the circus were to sell 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

Since the question is asking for a percentage and there is an unknown in the problem -- the ticket price -- we can plug in for the unknown.

Let ticket price = 20. Now let's take this number through the problem:

220 tickets for this month's performance at its usual price 220 * 20 = 4400

the revenue from sales would be 10% greater than that collected last month. 4400 is 10% more than 4000, so last month = 4000

If the circus raised the ticket price by 5% 5/100 * 20 = 1, so raised ticket price = 20+1 = 21

and sold only 200 tickets as a result 200*21 = 4200

what percent less would last month's revenue be compared to this month's revenue? % decrease = difference/(larger number) * 100 = (4200-4000)/4200 * 100 = 200/42 = 100/21

The correct answer is C.

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avinash_hep@yahoo.com · Answer

Another approach -

From 1st statement, I get to find that the number of tickets sold last month = 200 (@ $x per ticket),

Given that this month, the same 200 tickets are sold but at 5% higher (@ $1.05x per ticket), algebraically,

200 * 1.05x - percent (200 * 1.05x) = 200 * x

which gives the "percent" as 100/21. Answer C.

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