If by increasing the price of a ticket in the ratio 8 : 11 the number ...
Let the price of the ticket be 8x and revised price be 11x (Since the ratio given is 8 ∶ 11)
Number of tickets sold be 23y and revised number be 21y,
⇒ Revenue before increase in price = 8x × 23y = 184xy
⇒ Revenue after increase in price = 11x × 21y = 231xy
Given, 184xy = 36800
⇒ xy = 200
⇒ Increased revenue = 231xy = 231 × 200 = Rs. 46200
∴ Increase in revenue = 46200 - 36800 = Rs. 9400
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If by increasing the price of a ticket in the ratio 8 : 11 the number ...
Increase in Price of Ticket vs. Number of Tickets Sold
Let's assume the initial price of a ticket is P and the initial number of tickets sold is Q.
According to the given information, the ratio of the increase in the price of a ticket is 8:11, and the ratio of the number of tickets sold is 23:21.
Increase in Price:
The ratio of the increase in the price of a ticket is 8:11.
Let's assume the increase in price is x.
So, the new price of a ticket will be P + x.
Decrease in Number of Tickets Sold:
The ratio of the number of tickets sold is 23:21.
Let's assume the decrease in the number of tickets sold is y.
So, the new number of tickets sold will be Q - y.
Calculation of Increase in Revenue:
Initial Revenue = Initial price of a ticket x Initial number of tickets sold
= P x Q
New Revenue = New price of a ticket x New number of tickets sold
= (P + x) x (Q - y)
As per the given information, the initial revenue is Rs. 36,800.
Therefore, we have:
P x Q = 36,800
We need to find the increase in revenue, which is the difference between the new revenue and the initial revenue:
Increase in Revenue = New Revenue - Initial Revenue
= (P + x) x (Q - y) - (P x Q)
Simplifying the expression:
= (PQ + Px - Qy - xy) - PQ
= Px - Qy - xy
Calculation of Increase in Revenue:
We know that Increase in Revenue = Px - Qy - xy.
Now, let's substitute the given ratios:
Px - Qy - xy = (8/11)x - (23/21)y - (8/11)(23/21)x
To find the value of the increase in revenue, we need to know the values of x and y, which are not provided in the question. Therefore, we cannot determine the exact increase in revenue.
However, we can still analyze the answer options and select the appropriate one based on the given information.
Option B: 9400
Since we cannot determine the exact increase in revenue, we can check if the value of 9400 is feasible.
Let's assume the increase in price is 1100 and the decrease in the number of tickets sold is 1000.
Plug in these values in the equation:
Px - Qy - xy = (1100/11) - (1000/21) - (1100/11)(23/21)
= 100 - 47 - 100
= -47
The value obtained is negative. Since revenue cannot be negative, option B (9400) is not feasible.
Therefore, without the values of x and y, we cannot determine the exact increase in revenue. The given options do not provide a feasible answer based on the given information.