A merchant prices a television at 60 percent above wholesale. For a Presidents' Day sale, the merchant marks the television down by 25 percent. If he sells the television during the Presidents' Day sale, what percentage over the wholesale price will he have earned?
A. 75
B. 50
C. 35
D. 25
E. 20
The OA is option E.
This is a very real question. I would like to know how to solve it? Experts, may you give me a detailed explanation here? I'd be thankful.
Hi Vincen,
Let's take a look at your question.
Let the wholesale price of the television be '$x", then,
$$\text{Price of television with 60% increase}=x+60\%x=x+0.6x=1.6x$$
At Presidents' Day sale, the television is marked down by 20%.
Let's first calculate the discount offered at Presidents' Day sale,
$$Discount=\left(1.6x\right)\left(25\%\right)$$
$$Discount=\left(1.6x\right)\left(0.25\right)$$
New Price after discount will be:
$$\text{New Price after discount} =\ 1.6x-\left(1.6x\right)\left(0.25\right)$$
$$\text{New Price after discount}=\ 1.6x\left(1-0.25\right)$$
$$\text{New Price after discount} =\ 1.6x\left(0.75\right)$$
$$\text{New Price after discount} =\ 1.2x$$
To find the percentage earned over the whole sale price, we will rewrite this expression,
$$\text{New Price after discount} =\ (1+0.2)x$$
$$\text{New Price after discount} =\ (1+\dfrac{20}{100})x$$
$$\dfrac{20}{100} \text{represents 20 percent.}$$
Therefore, the merchant earned 20% profit over the whole sale price.
Hence, Option E is correct.
Hope it helps.
I am available if you'd like any follow up.
