Question

What should be the minimum mark up percentage such that after giving the discount of $\dfrac{{200}}{3}\% $, there will neither be a loss nor a profit?
A) $133.3\% $
B) $100\% $
C) $150\% $
D) $200\% $
E) $300\% $

Answer 1

Hint: Here, in the given question, we need to find the minimum mark up percentage such that after giving the discount of $\dfrac{{200}}{3}\% $, there will be neither a loss nor a profit. Markup is the difference between the list price (the highest price a consumer will be charged) and cost price. We will first assume the list price is $x$. From this we will find the value of selling price, as it’s already mentioned in the question there is no profit or loss, so selling price will be equal to cost price. And we know by the definition of markup that markup is equal to list price – cost price, so using this we will calculate the markup percentage.

Complete step by step solution:
Let the list price of the product be $Rs.x$.
Discount = $\dfrac{{200}}{3}\% $ of list price = $\dfrac{{200}}{3}\% \, of \,{\text{ }}x$ = $\dfrac{{200}}{3} \times \dfrac{1}{{100}} \times x$= $\dfrac{{2x}}{3}$
As we know selling price = List price – discount. Therefore, we get
Selling price = $Rs.\left( {x - \dfrac{{2x}}{3}} \right)$
$ = Rs.\dfrac{x}{3}$
As it is already mentioned in the question that there is no gain or loss. Therefore, cost price = selling price.
$ \Rightarrow C.P = Rs.\dfrac{x}{3}$
So, from here we can conclude that for $\dfrac{x}{3}$ as cost price, the list price is $x$.
Let’s take $Rs.100$ as the cost price (just for the ease of calculation), Then we have,
$\dfrac{x}{3} = 100$
$ \Rightarrow x = 300$
As we know $x$ is the list price. Therefore, for $100$ as cost price, list price = $Rs.300$
Difference between the list price and cost price = $Rs.\left( {300 - 100} \right) = Rs.200$
Therefore, minimum markup percentage = $200\% $. So, option (D) is correct.

Note:
> Remember that the list price is the highest price a consumer will be charged and cost price is the total amount of money that it costs a manufacturer to produce a given product.
> Note that the discount is always calculated w.r.t. list price.
> Here, we didn’t used the direct formula of markup percentage, which is $Markup = \dfrac{{S.P}}{{C.P}} - 1$, because as its mentioned in the question there is no gain or loss. If we had used this formula, the markup percentage would be zero.