Question

A discount of 25% on one shirt is the same as discount of 50% on a second shirt. The costs of the two shirts can be:

• A. $\$50,\$100$
• B. $\$30,\$60$
• C. $\$50,\$25$
• D. $\$70,\$35$

Answer 1

Answer: (C), (D)

$\$70,\$35$

Let the prices of two shirts be X and Y

Discount amount of first shirt $=25\%\text{of}X$
$=\frac{25}{100}\times X=\frac{25}{25\times 4}\times X$
$=\frac{1}{4}\times X$
$=\frac{X}{4}$

Discount amount of second shirt $=50\%\text{of}Y$
$=\frac{50}{100}\times Y=\frac{50}{50\times 2}\times Y$
$=\frac{1}{2}\times Y$
$=\frac{Y}{2}$

Give, discount amount of both the shirts are equal
$\therefore \frac{X}{4}=\frac{Y}{2}$
$\Rightarrow \frac{X}{Y}=\frac{4}{2}$
$\Rightarrow \frac{X}{Y}=\frac{2}{1}$

Now, lets check all the options.
$\left(A\right)X=50,Y=100$
$\Rightarrow \frac{X}{Y}=\frac{50}{100}$
$\Rightarrow \frac{X}{Y}=\frac{50}{50\times 2}$
$\Rightarrow \frac{X}{Y}=\frac{1}{2}\ne \frac{2}{1}$
$\to \text{REJECTED}$

$\left(B\right)X=30,Y=60$
$\Rightarrow \frac{X}{Y}=\frac{30}{60}$
$\Rightarrow \frac{X}{Y}=\frac{30}{30\times 2}$
$\Rightarrow \frac{X}{Y}=\frac{1}{2}\ne \frac{2}{1}$
$\to \text{REJECTED}$

$\left(C\right)X=50,Y=25$
$\Rightarrow \frac{X}{Y}=\frac{50}{25}$
$\Rightarrow \frac{X}{Y}=\frac{25\times 2}{25}$
$\Rightarrow \frac{X}{Y}=\frac{2}{1}$
$\to \text{ACCEPTED}$

$\left(D\right)X=70,Y=35$
$\Rightarrow \frac{X}{Y}=\frac{70}{35}$
$\Rightarrow \frac{X}{Y}=\frac{35\times 2}{35}$
$\Rightarrow \frac{X}{Y}=\frac{2}{1}$
$\to \text{ACCEPTED}$