Price of a movie ticket has increased by 6%, as a result, there was a reduction of 4% in the audience for the show. As an overall effect, revenue of the movie hall has increased by Rs. 94. Find the initial revenue of the movie hall.5860386053405640
Question
Price of a movie ticket has increased by 6%, as a result, there was a reduction of 4% in the audience for the show. As an overall effect, revenue of the movie hall has increased by Rs. 94. Find the initial revenue of the movie hall.5860386053405640
Solution
Let's denote the initial price of a movie ticket as P and the initial number of audience as N. The initial revenue of the movie hall is then P*N.
After the price increase, the price of a movie ticket becomes P + 0.06P = 1.06P. The number of audience becomes N - 0.04N = 0.96N. The new revenue of the movie hall is then 1.06P * 0.96N.
According to the problem, the new revenue is Rs. 94 more than the initial revenue, so we have the equation:
1.06P * 0.96N = P*N + 94
Solving this equation for P*N (the initial revenue), we get:
P*N = 1.06P * 0.96N - 94
Since P and N are positive, we can divide both sides of the equation by 1.06 * 0.96 to get:
P*N = (1.06 * 0.96N * P - 94) / (1.06 * 0.96)
This equation tells us that the initial revenue of the movie hall is Rs. 94 less than the new revenue divided by 1.06 * 0.96. However, without knowing the values of P and N, we cannot calculate a numerical value for the initial revenue.
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