If a circus sells all of its 220 tickets for this month's performance

Question

If a circus sells all of its 220 tickets for this month's performance at the regular price, the revenue from these sales would exceed the revenue from the previous month by 10%. If the circus were to increase the ticket price by 5% and only sell 200 tickets, by what percentage would the revenue of the previous month be less compared to this month's revenue?

A.  2

B.  4

C.  \frac{100}{21}

D.  5

E.  \frac{11}{2}

Bunuel · Accepted Answer

If a circus sells all of its 220 tickets for this month's performance at the regular price, the revenue from these sales would exceed the revenue from the previous month by 10%. If the circus were to increase the ticket price by 5% and only sell 200 tickets, by what percentage would the revenue of the previous month be less compared to this month's revenue?

A.  2

B.  4

C.  \frac{100}{21}

D.  5

E.  \frac{11}{2} 
 
For percentage questions like this one, it's almost always better to plug in some smart numbers rather than trying to build an equation.
 
Assume the usual ticket price is $20 (we choose $20 because $20 plus 5% equals $21, an integer, which makes calculations easier). With this price, this month's revenue for 220 tickets would be  220*$20 = $4,400 , which we are told is 10% greater than the revenue collected previous month. Hence,  previous month's revenue was  \frac{$4,400}{1.1} = $4,000  .
 
If the circus were to raise the ticket price by 5%, the new price would be $21. Therefore,  the actual revenue from selling 200 tickets would be  200 * $21 = $4,200  .
 
To find out what percent less previous month's revenue would be compared to this month's revenue, we calculate the following:  	ext{percent}=\frac{4,200-4,000}{4,200}*100=\frac{100}{21}\% .
 
Answer: C.

KarishmaB · Answer

This is what comes to mind when I read this question:

"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."

220 tickets at usual price make 10% extra revenue. In case last month the tickets were sold at usual price, they would have sold 200 tickets (10% extra revenue would be due to 10% extra tickets sold if the price is the same)

"If the circus raised the ticket price by 5% and sold only 200 tickets as a result"

If the circus sold the same number of tickets as sold last month but increased the price by 5%, the revenue would also increase by 5%. (Revenue increases by either increasing the number of tickets or increasing the price or both)

"what percent less would last month's revenue be compared to this month's revenue" 
The question isn't the % by which this month's revenue is greater (which we know is 5%). The question is by what percent is last month's revenue less?
If last month's revenue = 100, this month's revenue = 105
Last revenue is less by 5/105 * 100 = 100/21%

JeffTargetTestPrep · Answer

We can let p = the usual price per ticket and r = revenue last month

So the normal revenue would be 220p and we can create the equation:

220p = 1.1r

200p = r

When the ticket price is raised 5%, the revenue is 1.05p(200) = 210p.

So the percent change from last month would be (200p - 210p)/210p x 100 = -10/210 x 100 = -1000/210 = -100/21, which corresponds to a revenue that is 100/21 percent less than this month’s revenue.

Answer: C

GMATNinja · Answer

Here's a video explanation. Enjoy!

https://www.youtube.com/watch?v=LYf9xAlyK90

GMATGuruNY · Answer

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. 
For the usual ticket price to yield 10% more in revenue, the number of tickets sold this month must be 10% greater than the number sold last month.
Since 220 is 10% greater than 200, the number of tickets sold last month = 200.

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? 
Since the number of tickets sold is the same as that sold last month -- 200 -- raising the ticket price by 5% will increase the total revenue by 5%.
Let last month's revenue = $100, implying that the revenue yielded by this month's 5% higher ticket price = $105.
Percent decrease from 105 to 100  = \frac{Difference}{Original }* 100 = \frac{5}{105} * 100 = \frac{100}{21}

C

Archit3110 · Answer

let price per ticket be 100$ and 5% increase ; 105$
220*100 ; 220,00 last year revenue must be 220,00/1.1 ; 200,00 $
with price increase $105 tickets sold 200 ; 21,000 
21000-20000/21000 ; 1000/21000 ;1/21*100 
option C ; 100/21

Kinshook · Answer

manalq8 
Given: 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.
Asked: 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?
Let the ticket's usual price be p.

Tickets sold this month = 220 tickets
Revenue this month = 220p

Revenue last month = 220p/1.1 = 200p

Ticket price after raising by 5% = 1.05p
Revenue after selling 200 tickets = 1.05p*200 = 210p

Difference in last month's revenue and this month's revenue = 210p - 200p = 10p
The percent less would last month's revenue be compared to this month's revenue = 10p/210p *100 = 1000/210 = 100/21%

IMO C

Dheeraj_079 · Answer

Lets assume the cost per ticket is $ x.
Total revenue earned = $ 220x 
This months revenue was 10% greater than last months

Last months revenue = $220x / 1.1 = $200x

Revenue earner for 200 tickets at 5 % increase in price = $ 200x* 1.05
Percentage = (200x*1.05 - 200x)/(200x*1.05)*100
                 = 100/21

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If a circus sells all of its 220 tickets for this month's performance

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If a circus sells all of its 220 tickets for this month's performance

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards