Question

A tradesman gives \[4\% \] discount on the marked price and gives 1 article free for buying every 15 articles thus gain \[35\% \]. The marked price is above the cost price by:
A. \[20\% \]
B. \[39\% \]
C. \[40\% \]
D. \[50\% \]

Answer 1

Hint: First of all, find the total discount gets by the tradesmen. Then find the cost price of the article can be calculated by using the formula \[{\text{CP}} = \dfrac{{100}}{{100 + {\text{Gain% }}}} \times {\text{SP}}\]. Then calculate the extra mark price which is the difference of market price and the cost price. So, use this concept to reach the solution of the given problem.

Complete step-by-step answer:

In the given question
Let the market price = Rs.100

Here \[4\% \] on Rs.100 is Rs.4

So, the price after discount of \[4\% \] = Rs.100 – Rs.4 = Rs.96

But again, he gives 1 article free on buying 15 articles, it means he gets a discount of 1 article on every set. So, the total set contains 16 articles.

Therefore, discount on Rs.96 \[ = \dfrac{{96}}{{16}} = {\text{ Rs}}{\text{. 6}}\]

Therefore, the total discount = Rs. 4 + Rs. 6 = Rs. 10

So, the discount percent is \[10\% \].
Hence, the selling price = Rs.100 – Rs. 10 = Rs. 90

We know that cost price \[{\text{CP}} = \dfrac{{100}}{{100 + {\text{Gain% }}}} \times {\text{SP}}\]

Given gain percentage is \[35\% \]
\[
   \Rightarrow {\text{CP}} = \dfrac{{100}}{{100 + 35}} \times 90 \\
   \Rightarrow {\text{CP}} = \dfrac{{100}}{{135}} \times 90 \\
  \therefore {\text{CP}} = {\text{ Rs}}{\text{. }}\dfrac{{200}}{3} \\
\]

Hence, extra mark price \[ = {\text{ Rs}}{\text{. }}100 - {\text{ Rs}}{\text{. }}\dfrac{{200}}{3} = {\text{ Rs}}{\text{. }}\dfrac{{100}}{3}\]

Thus, percentage increase on Rs. 100 \[ = \dfrac{{\dfrac{{100}}{3}}}{{\dfrac{{200}}{3}}} \times 100 = \dfrac{{100}}{3} \times \dfrac{3}{{200}} \times 100 = 50\% \]

Thus, the correct option is D \[50\% \].

Note: Here we have considered the market price as Rs.100 so that we can calculate the discount and gain percentage easily. The total discount is the sum of discount on the marked price and the discount on the set of articles.