Question

The number of seats in a movie hall is increased by $25\%$ and the price on ticket is decreased by $10\%$ what will be the effect on the revenue?

Answer 1

Let $x$ and $y$ be the No. of seats and price on $1$ ticket respectively.

Total revenue $=xy$

When seat is increased by $25\%$, i.e.,

$x^{\prime }=x+\frac{25}{100}\times x=x+\frac{x}{4}=\frac{5x}{4}$

And the price on ticket is decreased by $10\%$, i.e.,

$y^{\prime }=y-\frac{10}{100}\times y=y-\frac{y}{10}=\frac{9y}{10}$

Therefore,

Total revenue $=x^{\prime }\times y^{\prime }=\frac{5x}{4}\times \frac{9y}{10}=\frac{9xy}{8}=xy+\frac{xy}{8}$

Hence the total revenue is increased by $\frac{xy}{8}$, i.e., $12.5\%$.