Question

A customer paid \[\$24\] for a dress. If that price represented a 25 percent discount on the original price of the dress, what was the original price of the dress?
(A) \[\$28\]
(B) \[\$30\]
(C) \[\$31.25\]
(D) \[\$32\]

Answer 1

Hint: Assume that the original price of the dress is \[\$x\] . The customer purchases the dress at a discount of 25%, it means that the price at which the customer bought the dress is 25% less than the original price. So, the price at which the customer bought the dress is equal to \[\$x\]- 25% of \[\$x\] . It is given that the price at which the customer bought the dress is \[\$24\] . Now, solve it further and get the value of x.

Complete step-by-step answer:
According to the question, it is given that a customer paid \[\$24\] for a dress after getting a discount of 25%.
The price at which the customer bought the dress = \[\$24\] ………………………………(1)
The percentage of the discount that the customer got = 25% …………………………….(2)
Let us assume that the original price of the dress is \[\$x\] .
The customer purchases the dress at a discount of 25%, it means that the price at which the customer bought the dress is 25% less than the original price. So,
The price at which the customer bought the dress = \[\$x\]- 25% of \[\$x\] = \[\$\left(x-\dfrac{25}{100}x\right)\] = \[\$\left(\dfrac{100x-25x}{100}\right)=\$\dfrac{75x}{100}=\$\dfrac{3x}{4}\] ………………………………….(3)
From equation (1), we also have the price at which the customer bought the dress.
Now, on comparing equation (1) and equation (3), we get
\[\begin{align}
  & \Rightarrow \$24=\$\dfrac{3x}{4}\\&\Rightarrow\dfrac{24\times4}{3}=x\\&\Rightarrow8\times4=x\\&\Rightarrow32=x\\\end{align}\]
Therefore, the original price of the dress is \[\$32\] .
Hence, the correct option is (D).

Note:We can also solve this question using the fraction method.
The percentage of the discount given = 25%.
Now, converting 25% into a fraction, we get
25% = \[\dfrac{25}{100}=\dfrac{1}{4}\] ……………………………(1)
As 25% of the discount was given, it means that a fraction of \[\dfrac{1}{4}\] is removed from the price.
The remaining fraction = \[1-\dfrac{1}{4}=\dfrac{4-1}{4}=\dfrac{3}{4}\]…………………………………..(2)
After allowing a discount of \[\dfrac{1}{4}\], the customer paid \[\$24\]. It means \[\dfrac{3}{4}\]th of the original price of the dress is \[\$24\] .
\[\dfrac{3}{4}\]th part of the original price of the dress = \[\$24\] .
Now, using the unitary method,
The whole part of the original price of the dress = \[\dfrac{\$24}{\dfrac{3}{4}}=\dfrac{\$24\times4}{3}=\$8\times4=\$32\] .
Therefore, the original price of the dress is \[\$32\] .
Hence, the correct option is (D).