Question

A tradesman gives 4 % discount on his marked price and gives 1 article free for buying every 15 articles and thus gains 35 %. By what percent is the marked price increased above the cost price?
(a) 50 %
(b) 40 %
(c) 60 %
(d) 80 %

Answer 1

Hint: First of all find the selling price of 15 articles by cost price of 16 articles and 35 % gain. Now, take the marked price as a cost price and calculate the selling price for this after a 4 % discount. Now, by unitary method, find the actual marked price and compare it with the cost price.

Complete step-by-step answer:

Here, we are given that a tradesman gives a 4 % discount on his marked price and gives 1 article free for buying every 15 articles and thus gains 35 %. We have to find the percent by which the marked price is increased above the cost price. Before proceeding with this question, we must know the following terms:
Cost Price (C.P): This is the price at which the article is purchased by shopkeeper/seller
Selling Price (S.P): This is the price at which the article is sold by the shopkeeper/seller.
Profit or Gain = If the selling price is more than the cost price, the difference between them is the profit / increased gain.
The formula for gain and gain % is as follows:
Profit / Gain = S.P – C.P
Also, Gain % = \[\dfrac{Gain}{C.P}\times 100\]
Marked Price: Marked price is the price that a shopkeeper marks in the given item for the consumer to see. Marked price after the discount becomes the actual selling price.
Discount: Discount is the kind of reduction or deduction in the cost price of the product. The discount rate is given in percentage.
Selling Price = Marked Price – Discount
\[\text{Discount}=\dfrac{\left( \text{Discount Percentage} \right)\times \text{Marked Price}}{100}\]
Now, let us consider our question. Let us take the cost price of 1 article as 100 Rs.
So, we get C.P of 16 articles as \[16\times 100=Rs.1600\]
Now, we are given that he earned a 35 % profit on 15 articles because he has given the 16th article for free. We know that S.P = Gain + C.P
So, we get, S.P of 15 articles (16th article for free) = Gain + C.P of 16 articles……(i)
We know that Gain % = \[\dfrac{Gain}{C.P}\times 100\]
So, we get,
\[35=\dfrac{Gain}{1600}\times 100\]
\[Gain=16\times 35=Rs.560\]
By substituting the value of gain and cost price in equation (i), we get,
Selling Price of 15 articles = (560 + 1600) = Rs. 2160
So, we get a selling price of 1 article \[=\dfrac{2160}{15}\] = Rs. 144.
Now, let us suppose that the marked price of each article is Rs. 100, that is equal to the cost price.
We know that,
\[\text{Discount}=\dfrac{\left( \text{Discount Percentage} \right)\times \text{Marked Price}}{100}\]
We are given that he gives 4 % on the marked price. So, we get,
\[Discount=\dfrac{4\times 100}{100}\]
= Rs. 4
We know that S.P = Marked price – Discount
So, we get,
S.P = 100 – 4
S.P = Rs. 96
This means that, for a selling price of Rs. 96, the marked price is Rs. 100.
So, for the selling price of Re 1, the marked price would be Rs. \[\dfrac{100}{96}\].
We know that our actual selling price is Rs. 144.
So, for the selling price of Rs. 144, marked price \[=\left( 144\times \dfrac{100}{96} \right)Rs\]
= Rs. 150
So, we get the actual marked price = Rs. 150.
So, the percentage by which the marked price is above cost price
\[=\left[ \dfrac{\left( \text{Marked Price} \right)-\left( \text{Cost Price} \right)}{\left( \text{Cost Price} \right)} \right]\times 100\]
\[=\left( \dfrac{150-100}{100} \right)\times 100\]
= 50 %
Hence, option (a) is the right answer.

Note: In this question, students must note that in one formula, we have taken S.P of 15 articles instead of C.P of 16 articles, because the shopkeeper gave the 16th article for free. So this point must be taken care of. Also, apart from taking the variable for cost price, selling price, etc. it is always better to take cost price as Rs. 100 and proceed with the solution to easily calculate the various percentages.