Question

A dealer allows a discount of 10% and still gains 5%. What percent above the cost price must his goods be marked?
A. 15%
B. 20%
C. \[16\dfrac{2}{3}\%\]
D. 50%

Answer 1

Hint: From the formula of selling price find the value of marked price which is the price on the label of the particle. Thus to get the required percentage subtract cost price from the marked price.

Complete step-by-step answer:

Let us consider the cost price and the selling price. Cost price is the price at which an article is purchased. Selling price is the price at which an article is sold.

Thus lets the cost price be Rs. 100.

Similarly, let us take selling price as Rs. 10.5

We have been given a discount as 10%.

We know the formula,

\[SP=MP\dfrac{(100-d)}{100}\]

where MP is the marked price. It is the price on the label of an article. This is the price at which the product is intended to be sold. If there is some discount given on this price and the actual selling price of the product may be less than the marked price.

Selling price (SP) = Marked price (MP) – discount

\[\begin{align}

  & SP=MP\dfrac{(100-d)}{100} \\

 & \therefore MP=\dfrac{SP\times 100}{100-d} \\

\end{align}\] \[\because SP=Rs.105\]

\[=\dfrac{105\times 100}{100-10}=\dfrac{10500}{90}=\dfrac{350}{3}\]

Thus required percentage,

\[=\dfrac{MP-CP}{100}\times 100\]

\[MP-CP=\dfrac{350}{3}-100=\dfrac{350-300}{3}=\dfrac{50}{3}=16\dfrac{2}{3}\]

Thus required % \[=\dfrac{16{}^{2}/{}_{3}}{100}\times 100=16\dfrac{2}{3}\%\].

Thus, he should mark his goods \[16\dfrac{2}{3}\%\] above the CP.

Option C is the correct answer.

Note: In the profit and loss section, the cost of a product is very crucial. If you have marked the cost of the product wrong, you may not see any profit at all. If a discount is offered, then the marked price should be greater than the selling price.