Question

The ratio of the cost price and the marked price of an article is 2:3 and the ratio of the percentage profit and percentage discount is 3:2. What is the discount percentage?

Answer 1

Hint: We will first let the common factor of cost price and marked price be 10 and let S.P be $x$. Then, find the profit percentage using the formula $\dfrac{{{\text{S}}{\text{.P - C}}{\text{.P}}}}{{{\text{C}}{\text{.P}}}} \times 100$ and discount percentage $\dfrac{{{\text{M}}{\text{.P - S}}{\text{.P}}{\text{.}}}}{{{\text{M}}{\text{.P}}}} \times 100$ in terms of $x$. Then, use the given condition to find the value of $x$ and hence calculate the discount percentage.

Complete step by step Answer:

We are given that the ratio of cost price and marked price is 2:3
Let the common factor of the prices be 10
Then, the cost price is 20 and the marked price is 30
Let S.P be $x$
Then, we know that profit percent is $\dfrac{{{\text{S}}{\text{.P - C}}{\text{.P}}}}{{{\text{C}}{\text{.P}}}} \times 100$
Therefore, profit percent is $\dfrac{{x - 20}}{{20}} \times 100$
Also, the discount percent is $\dfrac{{{\text{M}}{\text{.P - S}}{\text{.P}}{\text{.}}}}{{{\text{M}}{\text{.P}}}} \times 100$
Therefore, the discount percentage is $\dfrac{{30 - x}}{{30}} \times 100$
We are also given that the ratio of percentage profit and percentage discount is 3:2.
$\dfrac{{\dfrac{{x - 20}}{{20}} \times 100}}{{\dfrac{{30 - x}}{{30}} \times 100}} = \dfrac{3}{2}$
On simplifying the above equation, we get,
$
  \dfrac{{x - 20}}{{20}} \times \dfrac{{30}}{{30 - x}} = \dfrac{3}{2} \\
   \Rightarrow x - 20 = 30 - x \\
   \Rightarrow 2x = 50 \\
   \Rightarrow x = 25 \\
$
Then, we calculate the discount percentage by substituting the value in the formula $\dfrac{{30 - x}}{{30}} \times 100$
$\Rightarrow$$\dfrac{{30 - 25}}{{30}} \times 100 = \dfrac{5}{{30}} \times 100 =16.66\% $

Note: When selling price is more than the cost price, profit is made, that is, profit is made on the cost-price of an object. Whereas, the discounted price is the difference between the marked price and the selling price of an object and the discount is always on the marked price. Many students make mistakes in considering selling price and marked price as the same quantity which is incorrect.