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 \[10\% \] discount.
A.\[11\dfrac{1}{7}\]
B.\[13\dfrac{2}{7}\]
C.\[15\dfrac{5}{7}\]
D.\[17\dfrac{6}{7}\]

Answer 1

Hint: Here, we will find the selling price. It 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 cost price is greater than the selling price, 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:
Given that the original marked price is Rs. 18,000.
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 bears with overheads..
\[
  {\text{C.P.}} = 12600 + 950 + 450 \\
   = {\text{Rs }}14000 \\
 \]
Thus, the cost price of an article is Rs. 14000.
We will now find the selling price at which the shopkeeper sells after the\[10\% \] discount using the above formula of selling price.
\[
  {\text{S.P.}} = 18000 - \dfrac{{10}}{{100}} \times 18000 \\
   = 18000 - 1800 \\
   = {\text{Rs }}16200 \\
 \]
Since we know that the selling price is greater than the cost price, there is a profit.

We know that the profit is calculated by the difference of cost price of an article from selling price of an article.
Subtracting the values of cost price \[{\text{C.P.}}\] from the selling price \[{\text{S.P.}}\] to find the profit of a given article, we get
\[
  {\text{Profit}} = 16200 - 14000 \\
   = {\text{Rs }}2200 \\
 \]
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. in the above formula for profit percentage of the given article, we get
\[
  {\text{Profit}}\% = \dfrac{{2200}}{{14000}} \times 100 \\
   = \dfrac{{11}}{{70}} \times 100 \\
   = \dfrac{{110}}{7}\% \\
 \]
Simplifying the above fraction to find the profit percentage, we get
\[{\text{Profit}}\% = 15\dfrac{5}{7}\% \]
Thus, we get that the profit from an article is \[15\dfrac{5}{7}\% \].

Hence, the option is C 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 subtract 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.