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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

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? _________________

Trying to make CR and RC my strong points

"If you want my advice, Peter," he said at last, "you've made a mistake already. By asking me. By asking anyone. Never ask people. Not about your work. Don't you know what you want? How can you stand it, not to know?" Ayn Rand

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%).

"If you want my advice, Peter," he said at last, "you've made a mistake already. By asking me. By asking anyone. Never ask people. Not about your work. Don't you know what you want? How can you stand it, not to know?" Ayn Rand

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

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'.

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)

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 \(\frac{\text{Difference}}{\text{This Month}}\).

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%

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: \(percent=\frac{4,200-4,000}{4,200}*100=\frac{100}{21}%\).

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.

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