Question

A dealer offers a discount of 20% and still makes a profit of 20% and he further allows 4 articles free on the sale of 12 articles. Find the ratio of cost price to marked price.

Answer 1

Hint: Marked Price is the price which is listed on any article.Discount is always calculated with respect to the Marked Price.So In this question first we will calculate the Selling price after subtracting the Discount percentage from the Marked Price and then use the formula of Cost Price when Profit% is given

Complete step-by-step answer:
Selling Price $ = $ Marked Price $ - $ Discount%
Cost Price $ = \dfrac{{100 \times SP}}{{100 + P\% }} $
Let the marked price of the article be Rs \[x\]
Discount offered by the dealer $ = 20\% $ of $ x $ $ = \dfrac{{20}}{{100}} \times x = \dfrac{x}{5} $
Price after discount $ = x - \dfrac{x}{5} = \dfrac{{4x}}{5} $
Now the dealer gave 4 articles free on the purchase of 12 articles
So, the discount offered $ = \dfrac{4}{{16}} \times 100 = 25\% $
Hence the Selling price after giving 4 articles for free $ = \dfrac{{4x}}{5} - \dfrac{x}{5} = \dfrac{{3x}}{5} $
After giving Discount, the dealer still earns a profit of 20%
We know, Cost Price $ = \dfrac{{100 \times SP}}{{100 + P\% }} $
 $ \Rightarrow CP = \dfrac{{100 \times 3x}}{{(100 + 20) \times 5}} = \dfrac{x}{2} $
The Cost Price of the articles was Rs $ \dfrac{x}{2} $
Now Ratio of Cost Price to Marked Price $ = \dfrac{x}{2}:x $
Cost price : Marked Price $ = 1:2 $

Note: We can solve this question directly also by taking the value of the Marked price to be Rs 150 just as an example.
Marked Price $ = 150 $
Price after 20% discount $ = 150 - 20\% \times 150 = 120 $
Dealers allow a discount of 25% more in form of articles.
Final Selling price $ = 120 - 25\% \times 120 = 90 $
Hence Cost Price $ = \dfrac{{100 \times 90}}{{120}} = 75 $
Now $ CP:MP = 75:150 = 1:2 $