Question

The marked price of an article is Rs. 18,000 and is available in Delhi at \[30\% \] discount. A shopkeeper from Bhopal buys this article in Delhi and spends Rs. 950 on his travelling and Rs. 450 on the transportations, etc. of the article. Find the profit percent made by the shopkeeper, if he sells the article at Bhopal at the marked price.
A. \[20\dfrac{1}{3}\% \]
B. \[28\dfrac{4}{7}\% \]
C. \[33\dfrac{5}{2}\% \]
D. \[22\dfrac{9}{5}\% \]

Answer 1

Hint: Here, we will find the sale price is calculated using the formula, \[{\text{S.P.}} = {\text{Marked Price}} - \dfrac{{{\text{Discount Percentage}}}}{{100}} \times {\text{Marked Price}}\]. Then we will check if the costing price is greater than the selling price of the shopkeeper in Bhopal, then find the gain or loss percentage using \[{\text{Loss/Gain}}\% = \dfrac{{{\text{Loss/Gain}}}}{{{\text{C.P.}}}} \times 100\] from the given values.

Complete step by step answer:

We are given that the original marked price is Rs. 18,000 in the shop in Delhi.

We know that the sale price is calculated using the formula, \[{\text{S.P.}} = {\text{Marked Price}} - \dfrac{{{\text{Discount Percentage}}}}{{100}} \times {\text{Marked Price}}\].

We will now find the amount at which the shopkeeper buys an article in Delhi after \[30\% \] discount using the above formula.

\[
  {\text{S.P. of an article in Delhi}} = 18000 - \dfrac{{30}}{{100}} \times 18000 \\
   = 18000 - 5400 \\
   = {\text{Rs }}12600 \\
 \]

We will now find the total C.P. which the shopkeeper in Bhopal bears with overheads.

\[
  {\text{C.P.}} = 12600 + 950 + 450 \\
   = {\text{Rs }}14000 \\
 \]

Thus, the cost price of an article for the shopkeeper in Bhopal is Rs. 14000.

We know that the selling price is the marked price in Delhi, that is, Rs. 18,000.

Since we know that the selling price is greater than the costing price, there is a profit.

We know that the profit is calculated by the difference of the cost price of an article from the selling price of an article.

Subtracting the values of cost price \[{\text{C.P.}}\] of the shopkeeper in Bhopal from the selling price \[{\text{S.P.}}\] in Bhopal to find the profit of a given article, we get

\[
  {\text{Profit}} = 18000 - 14000 \\
   = {\text{Rs 40}}00 \\
 \]

We know that the formula to calculate the profit percentage is calculated as \[{\text{Profit}}\% = \dfrac{{{\text{Profit}}}}{{{\text{C.P.}}}} \times 100\], where C.P. is the cost price.

Substituting the values of Profit and C.P. of the shopkeeper in Bhopal in the above formula for profit percentage of the given article, we get

\[
  {\text{Profit}}\% = \dfrac{{4000}}{{14000}} \times 100 \\
   = \dfrac{2}{7} \times 100 \\
   = \dfrac{{200}}{7}\% \\
 \]

Simplifying the above fraction to find the profit percentage, we get

\[{\text{Profit}}\% = 28\dfrac{4}{7}\% \]
Thus, we get that the profit from an article is \[28\dfrac{4}{7}\% \].

Hence, the option is B will be correct.

Note: While solving these types of problems, the amount of discount given on the marked price is \[\dfrac{{{\text{Discount Percentage}}}}{{100}} \times {\text{Marked Price}}\] and then this amount is subtracted from the marked price in order to get the selling price. In this question, students must note that we have added all the expenses of transportation and travelling, while finding the cost price of an article. So this point must be taken care of.