Question

A circus earned Rs.150,000 in ticket revenue by selling 1800 VIP and standard tickets. They sold 25% more standard tickets than VIP tickets. If the revenue from standard tickets represents one – third of the total ticket revenue, what is the price of a VIP ticket?
(a) Rs.130
(b) Rs.125
(c) Rs.120
(d) Rs.110

Answer 1

Hint: Take V and S as the number of VIP and standard tickets sold. Now find the value of V and S by solving the equations formed. The price of a standard ticket sold is \[{{\dfrac{1}{3}}^{rd}}\] of total earnings. Thus find total cost of VIP ticket. The cost of 1 VIP ticket is the total cost of a VIP ticket by number of tickets.

Complete step-by-step answer:
Now here the circus sells two types of tickets. One is the VIP tickets and the rest are standard tickets. We need to make sure to differentiate between the price of tickets and the quantity of the tickets sold.
Let us consider ‘V’ as the VIP tickets sold and let S be the standard tickets sold. It is said that the circus sold a total of 1800 tickets. The circus sold 25% more standard tickets than VIP tickets.
Thus we can create two equations as,
Total number of ticket sold = 1800
i.e. V + S = 1800 – (1)
And 25% more of standard tickets are sold than VIP tickets.
Thus we can say that, S = 1.25V – (2)
Now put the value of S in equation (1) and find the number of VIP tickets.
\[\begin{align}
  & V+1.25V=1800 \\
 & 2.25V=1800\Rightarrow V=\dfrac{1800}{2.25}=800 \\
\end{align}\]
Thus we got the number of VIP tickets sold as 800.
\[\therefore \] Total number of standard tickets = Total tickets – number of VIP ticket sold
\[\therefore \] Total number of standard tickets = 1800 – 800 = 1000.
Thus they sold 800 VIP tickets and 1000 standard tickets.
Now we need to find the cost per VIP ticket sold. It is said that the circus earned Rs.150,000 in ticket revenue and the standard tickets represented one – third of the total revenue.
\[\therefore \] Standard tickets = \[\dfrac{1}{3}\times 150000=\ 50,000\]
Thus the total rate of standard tickets sold = Rs.50,000.
\[\therefore \] Cost of VIP ticket sold = 150000 – cost of standard sold = 150000 – 50000 = Rs.100,000.
\[\therefore \] The cost of 800 VIP tickets = Rs.100,000.
\[\therefore \] Cost of VIP ticket = \[\dfrac{100,000}{800}\] = Rs.125 per VIP ticket.
Thus we got the price of the VIP ticket as Rs.125.
\[\therefore \] Option (b) is the correct answer.

Note: Don’t get confused between the number of tickets and the price of tickets. First find the number of tickets then it would be easier to find the price of these tickets. If we are asked to find the cost of 1 standard ticket = \[\dfrac{50000}{1000}\] = Rs.50.