Question

The number of seats in a movie hall is increased by \[25\% \] and the price on tickets is decreased by \[10\% \]. What will be the effect on the revenue?

Answer 1

Hint: First, we will assume the number of seats and price of each ticket and then find the total revenue by multiplying them. Then we will use given conditions and then apply the formula to find the percentage, that is, \[{\text{Percentage}} = \dfrac{{{\text{Obtained Value}}}}{{{\text{Total Value}}}} \times 100\] to find the required value.

Complete step-by-step solution
It is given that the number of seats in a movie hall is increased by \[25\% \] and the price on tickets is decreased by \[10\% \].

Let us assume that the number of seats be \[x\] and the price of each ticket is Rs \[y\].

We will now calculate the total revenue collected by product of number of seats and price of each ticket.

\[{\text{Total revenue collected}} = {\text{Rs }}xy\]

Now finding the number of seats, which are increased by \[25\% \], we get

\[
  \left( {1 + \dfrac{{25}}{{100}}} \right)x = \left( {1 + 0.25} \right)x \\
   = 1.25x \\
 \]

Thus, the seats increase to \[1.25x\] seats.

We will now find the price of each ticket after the price is decreased by \[10\% \].

\[
  \left( {1 - \dfrac{{10}}{{100}}} \right)y = \left( {1 - 0.1} \right)y \\
   = 0.9y \\
 \]

Thus, the price of each ticket decreases to \[0.90y\].

Multiplying the increased number of seats and the decreased price of each ticket to find the total revenue collected, we get

\[1.25x \times 0.90y = 1.125xy\]

So now finding the increased revenue from the difference of new revenue and old revenue, we get

\[1.125xy - xy = {\text{Rs }}0.25xy\]

Here, we will use the formula to find the percentage, that is, \[{\text{Percentage}} = \dfrac{{{\text{Obtained Value}}}}{{{\text{Total Value}}}} \times 100\].

We will now find the increase in percentage from the increased revenue in the above formula for percentage.

\[
  {\text{Percentage increases = }}\dfrac{{0.125xy}}{{xy}} \times 100 \\
   = 0.125 \times 100 \\
   = 12.5\% \\
 \]

Therefore, the revenue increased by \[12.5\% \].

Note: In solving these types of questions, you should be familiar with the concept of purchasing, selling and the price percentage. The only step at which the student can make mistakes is where the increased percentage of the new revenue is to be calculated as it is sometimes confusing what is to be taken in the numerator and what in the denominator. Also, we are supposed to write the values properly to avoid any miscalculation.