cinema hall's revenue

bhumika.k.shah wrote:If the cinema hall 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 cinema hall 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

Answer is C

Different approaches welcomed!

Let x be the price Y be the number of tickets sold last month

and the question says 220x = (Yx) (1+10/100)

Y = 200

Now x(1+5/100)*200 is the new revenue

Last Months revenue = 200x

% last month's revenue is less compared to this month's revenue =(This Month's revenue - Last Months revenue/This Month's Revenue)*100

= (x(1.05)*200 - 200x)*100/ x(1.05)*200 = 10x*100/x*210 =100/21

Let's say: Price of ticket be 100 and revenue be X. So, from first statement, 220 * 100 = (110/100) * X. Solving gives X=20000.
As per the second statement, the 'new' revenue 200*105=21000.
To find percent change, [(21000-20000)/21000] * 100 = 100/21.

Or, alternatively, set up equations using variables. Let price of ticket be X and revenue be Y.
From first statement, 220*X=(110/100)*Y, which gives revenue=200X.
From second statement, 200*(105X/100)=210X which is the 'new revenue'.
To find percent change, [(210X-200X)/210X]*100 = 100/21.

pharmxanthan wrote:Let's say: Price of ticket be 100 and revenue be X. So, from first statement, 220 * 100 = (110/100) * X. Solving gives X=20000.
As per the second statement, the 'new' revenue 200*105=21000.
To find percent change, [(21000-20000)/21000] * 100 = 100/21.

Or, alternatively, set up equations using variables. Let price of ticket be X and revenue be Y.
From first statement, 220*X=(110/100)*Y, which gives revenue=200X.
From second statement, 200*(105X/100)=210X which is the 'new revenue'.
To find percent change, [(210X-200X)/210X]*100 = 100/21.

awesome explanations! thanks