Question

In a cinema hall, the charge per person is Rs.200. On the first day, only 60% of the seats were filled. The owner decided to reduce the price by 20% and there was an increase of 50% in the number of spectators the next day. The percentage increases in the revenue on the second day was
(A). 50
(B). 40
(C). 30
(D). 20

Answer 1

Hint – Assume the total number of seats to be 100 on the first day. Then find the revenue collected on the first day and second day, by multiplying the ticket price with the number of seats filled.

Complete step-by-step solution -
We have given the question- charge of ticket per person is Rs.200.
On the first day 60% of the seats were filled and the owner decided to reduce the price by 20% and there was an increase of 50% in the number of spectators.
Let the total number of seats be 100.
On the first day ticket price = Rs.200.
Seats filled = 60%
60% means $\dfrac{{60}}{{100}} \times 100 = 60$ {Since the total seats are assumed to be 100}
To find the total revenue earned multiply the no. of seats with the price of tickets.
Total revenue earned on the first day ${R_1} = 60 \times 200 = 12000$ .
On the second day ticket price was reduced to 20%.
So, now the ticket price is $200 - \dfrac{{20}}{{100}} \times 200 = 200 - 40 = 160$


Increase in the number of seats filled on the second day is 50% more than the first day.
So, the total number of spectators on the second day $60 + \dfrac{{50}}{{100}} \times 60 = 60 + 30 = 90$ {Since on the first day total no. of seats filled were 60}.
Revenue earned on the second day ${R_2} = 160 \times 90 = 14400$
Now the % increase in revenue is $ = \dfrac{{{R_2} - {R_1}}}{{{R_1}}} \times 100$
Now putting the value of R1 and R2 we get-
$
   = \dfrac{{14400 - 12000}}{{12000}} \times 100 \\
   = \dfrac{{2400}}{{12000}} \times 100 = 20\% \\
$
Therefore, the percentage increase in the revenue on the second day was 20%.
Hence, the correct option is D.
Note – Whenever such types of questions appear then first find out the total number of seats filled on the first day and then multiply it with the price of the ticket to find the revenue. Then find the number of seats filled when the price reduced to 20% and then again find the revenue. So, the increase in revenue will be obtained by using the standard formula, $\dfrac{{{R_2} - {R_1}}}{{{R_1}}} \times 100$ .