Question

13. The cost of a cinema ticket was + 5.00. This was reduced by 20%, with
the result that the total sale proceeds increased by 28%. What was the
percentage increase in attendence ?
(JAC., 2010)
(Ans. 60%]​

Answer 1

Step-by-step explanation:

cp =5

sale proceeds p = cp of ticket × no. of tickets sold = 5n

p=5n

n=p/5 = 0.2p

cp reduced by 20%

cp1= 5×(1-20%) = 5×(1-0.2) = 5×.8 =4

sale proceeds increased by28% = p1

= p×(1+28%) = 1.28p

let no of tickets increased by x%= n1= (1+x/100)n

p1 =n1×cp1

1.28p = 4×n1

n1= 1.28p/4 = 0.32p

% increase in n= n1 -n/n ×100

= (0.32p - 0.2p)/0.2p = 0.12p/0.2p

= 12/20 ×100 =60%

alternatively :

x-20-0.2x = 28

0.8x = 28+20=48

x = 48/0.8 = 60%