Problem Solving

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}


please explain in detail how do u come to the solution ....

Current month revenue
------------------------------------

Let the price be 5

Revenue=220*5=1100

This month revenue is 10% greater than last month.

Last month revenue=1000

Current month revenue after increasing the price
-----------------------------------------------------

Price is raised by 5%.So the new price is 5+5/100*5=5.25

Revenue=200*5.25=1050

Current month revenue=1050

Last month revenue=1000

1000[1+a/100]=1050

Solving we get a=5(ie) last month revenue is 5% less than current month revenue

Pick B

thanks for the explanation ..well can u explain why did u consider the initial price to be 5 ?

We can initial price as any random number.I picked 5 as it results in multiple of 100 which is easy to solve.

selango wrote:Current month revenue
------------------------------------

Let the price be 5

Revenue=220*5=1100

This month revenue is 10% greater than last month.

Last month revenue=1000

Current month revenue after increasing the price
-----------------------------------------------------

Price is raised by 5%.So the new price is 5+5/100*5=5.25

Revenue=200*5.25=1050

Current month revenue=1050

Last month revenue=1000

1000[1+a/100]=1050

Solving we get a=5(ie) last month revenue is 5% less than current month revenue

Pick B

Careful! You calculated the percent increase from 1000 to 1050: 1050 is 5% more than 1000. We need the percent decrease from 1050 to 1000. Using your numbers:

Current revenue = 1050
Last month's revenue = 1000

Percent decrease = Difference/Larger * 100 = 50/1050 * 100 = 100/21.

1000 is (100/21)% less than 1050.

The correct answer is C.

We could plug in any number for the ticket price. I chose $20 in order to avoid decimals:

This month's revenue = 220 * 20 = 4400
4400 is 10% more than 4000, so last month's revenue = 4000
Raised ticket price = 20 + (5/100 * 20) = 21
Revenue if only 200 tickets sold = 200*21 = 4200
% decrease = difference/larger * 100 = (200)/4200 * 100 = 200/42 = 100/21

The correct answer is C.

What's the source ?

GMATGuruNY wrote:

selango wrote:Current month revenue
------------------------------------

Let the price be 5

Revenue=220*5=1100

This month revenue is 10% greater than last month.

Last month revenue=1000

Current month revenue after increasing the price
-----------------------------------------------------

Price is raised by 5%.So the new price is 5+5/100*5=5.25

Revenue=200*5.25=1050

Current month revenue=1050

Last month revenue=1000

1000[1+a/100]=1050

Solving we get a=5(ie) last month revenue is 5% less than current month revenue

Pick B

Careful! You calculated the percent increase from 1000 to 1050: 1050 is 5% more than 1000. We need the percent decrease from 1050 to 1000. Using your numbers:

Current revenue = 1050
Last month's revenue = 1000

Percent decrease = Difference/Larger * 100 = 50/1050 * 100 = 100/21.

1000 is (100/21)% less than 1050.

The correct answer is C.

We could plug in any number for the ticket price. I chose $20 in order to avoid decimals:

This month's revenue = 220 * 20 = 4400
4400 is 10% more than 4000, so last month's revenue = 4000
Raised ticket price = 20 + (5/100 * 20) = 21
Revenue if only 200 tickets sold = 200*21 = 4200
% decrease = difference/larger * 100 = (200)/4200 * 100 = 200/42 = 100/21

The correct answer is C.

Yes Mitch..Thanks for correcting my mistake.