Question

Mark got a $30% $ discount on a movie ticket. When the price of the movie ticket increased by $50% $, the amount of discount in dollars remained the same. What is the percent discount he received on the new ticket price?
A.10
B.15
C.20
D.25
E.28

Answer 1

Hint: We will take the original cost of the movie ticket as an unknown quantity i.e., a variable. Next, we will find the discount price on the movie ticket using the formula of discount percentage. Then, we will find the new price of the ticket and using this we will find the percent discount on the new ticket price.

Formula used:
 ${\text{Discount% }} = \dfrac{{{\text{Discount Price}}}}{{{\text{Cost Price}}}} \times 100$

Complete step-by-step answer:
Let us assume that the original cost of the movie ticket is $\$ x$. It is given that Mark received a $30% $ on the ticket.
Using the formula, ${\text{Discount% }} = \dfrac{{{\text{Discount Price}}}}{{{\text{Cost Price}}}} \times 100$, we have
$30 = \dfrac{{{\text{Discount Price}}}}{x} \times 100$
Dividing both sides by 100, we get
 $ \Rightarrow \dfrac{{30}}{{100}} = \dfrac{{{\text{Discount Price}}}}{x} \times \dfrac{{100}}{{100}}$
$ \Rightarrow \dfrac{{30}}{{100}} = \dfrac{{{\text{Discount Price}}}}{x}$
On cross multiplication, we get
$ \Rightarrow $ Discount Price $ = \dfrac{{30}}{{100}}x = \$ 0.3x$
Now, the ticket price has increased by $50% $, so
The new ticket price $ = x + 50% $ of $x$
Converting percentage into fraction, we get
$ \Rightarrow $ The new ticket price $ = x + \dfrac{{50}}{{100}}x$
Converting the fraction into decimal, we get
$ \Rightarrow $ The new ticket price $ = x + 0.5x = \$ 1.5x$
It is given that the discount amount remains the same i.e., $\$ 0.3x$.
We now have to find the new discount percentage.
Substituting Discount price $ = \$ 0.3x$and Cost price $ = \$ 1.5x$ in the formula ${\text{Discount% }} = \dfrac{{{\text{Discount Price}}}}{{{\text{Cost Price}}}} \times 100$, we get
 Discount $% = \dfrac{{0.3x}}{{1.5x}} \times 100$
Dividing the numerator and denominator by $0.3$, we get
$ \Rightarrow $ Discount $% = \dfrac{1}{5} \times 100 = 20$
Therefore, the percent discount that Mark received on the new ticket is $20% $.
Thus, option C is the correct answer.

Note: We can also approach the above problem by assuming the original cost of the ticket as $\$ 100$.
As the discount is $30% $, the discount price will be $\$ 30$.
After the increase in the price of the ticket, the new cost is $\$ 150$.
The discount amount remains the same.
Now using the formula, ${\text{Discount% }} = \dfrac{{{\text{Discount Price}}}}{{{\text{Cost Price}}}} \times 100$, we get,
Discount $% = \dfrac{{30}}{{150}} \times 100$
Dividing the numerator and denominator by 30, we get
$ \Rightarrow $ Discount $% = \dfrac{1}{5} \times 100 = 20$