Question

A shopkeeper buys an article at a rebate of 20% on its marked price and then spends Rs. 300 on its transportation, etc. If he sells the article for Rs. 4,160 (including sales tax at the rate of 4% of the marked price), find the shopkeeper's profit as percent.
A) $10\dfrac{1}{5}\% $
B) $11\dfrac{3}{2}\% $
C) $14\dfrac{2}{7}\% $
D) $15\dfrac{6}{5}\% $

Answer 1

Hint: We approach this problem by making an equation by comparing the selling price of the article given and the selling price calculated by including the sales tax i.e. 4% of the marked price, due to which we will be able to calculate the marked price of the article. After that we will subtract a rebate of 20% of marked price from the marked price and then add the transportation charges to get the actual cost at which the shopkeeper purchased the article. Then we will just subtract the purchasing cost from the selling cost to get the profit made by the shopkeeper and then we will calculate the profit percent using the profit and the cost price of the article.

Complete step-by-step answer:
Let us suppose the marked price on the article be Rs. x
We know that Selling price of the article after the addition of sales tax of 4% of the marked price is Rs. 4160
So, generalizing the situation we get to know that
Marked price + 4% of the marked price = Selling price
$x + \dfrac{{4x}}{{100}} = 4160$
$\dfrac{{104x}}{{100}} = 4160$
$104x = 416000$
$x = \dfrac{{416000}}{{104}} = 4000$
So, x = 4000
Now, the marked price of the article = Rs. x = Rs. 4000
So, we have to subtract the rebate now which is 20% on the article’s marked price.
Price after subtracting the rebate $ = 4000 - \left( {\dfrac{{20 \times 4000}}{{100}}} \right) = 3200$
So, price after subtracting the rebate = Rs. 3200
Transportation charges so given = Rs. 300
We have to add them to the above price to calculate the actual price at which the shopkeeper purchased the article.
Cost price of the article $ = 3200 + 300 = 3500$
So, Cost price of the article = Rs.3500
Selling price of the article for the shopkeeper which is also the marked price = Rs. 4000
So, profit made by the shopkeeper = Selling price – Cost price = Rs. 4000 – Rs. 3500 = Rs. 500
Now, Profit made by the shopkeeper = Rs. 500
$Profit\% = \left( {\dfrac{{Profit}}{{\operatorname{Cos} t Price}}} \right) \times 100 = \left( {\dfrac{{500}}{{3500}}} \right) \times 100 = \dfrac{{100}}{7}\% = 14\dfrac{2}{7}\% $
Hence, profit made by the shopkeeper as percent is $14\dfrac{2}{7}\% $
Option C. $14\dfrac{2}{7}\% $ is the correct answer.

Note: For such types of questions just keep in mind we have to just calculate the cost price and the selling price of the article by the shopkeeper. Just keep in mind that we have to subtract the rebate which is a payback or a commission and add the necessary transportation charges. Also keep in mind that the profit is equal to Selling price – Cost price and we can calculate the profit as percent by simply using the formula
$Profit\% = \left( {\dfrac{{Profit}}{{\operatorname{Cos} t price}}} \right) \times 100$