Question

A wholesaler allows a discount of \[20\% \] on the list price to a retailer who sells it at \[5\% \] discount on the list price. If a customer paid Rs. \[114\] for an article, what profit is made by the retailer? Find, also the retailer's percentage profit on his cost.

Answer 1

Hint: In the given , we have given with the amount paid by the customer to the retailer , so we can let the price of the article be \[x\] , now \[95\% \] of \[x\] is equal to the amount paid the customer to the retailer , similarly , we can find the amount paid by the retailer to wholesaler , to find profit made by the retailer.

Complete step-by-step answer:
Let the price of the article be \[x\] .
Now , the price at which the retailer bought an article from the wholesaler will be \[ = \left[ {\left( {100 - 20} \right)\% } \right]\]of \[x\] .
On solving we get ,
\[ = 80\% \]of \[x\] .
On simplifying we get ,
\[ = Rs0.8x\]
Now , the amount at which the retailer sold the article to the customer will be
\[ = \left[ {100 - 5} \right]\% \]of \[x\] .
On solving we get ,
\[ = 95\% \]of \[x\] .
On simplifying we get ,
\[ = Rs0.95x\]
Now we have given the amount paid by the customer which will be equal to \[0.95x\] , so on equating we get ,
\[0.95x = 114\]
On simplifying we get ,
\[x = \dfrac{{114 \times 100}}{{95}}\]
On solving we get ,
\[x = \dfrac{{6 \times 100}}{5}\]
On solving further we get ,
\[x = 120\]
Now, using the value of \[x\] we will find out the amount paid by the retailer to wholesaler , therefore
\[ = Rs\left( {0.8 \times 120} \right)\]
On solving we get ,
\[ = Rs96\]
Now , profit made by the retailer will be equal to \[ = Rs\left( {114 - 96} \right)\]
On solving we get ,
\[ = Rs18\]
Now , for profit percentage we have formula
 \[ = \dfrac{{{\text{profit made on the article}}}}{{{\text{amount at which the article is bought }}\left( {C.P} \right)}} \times 100\]
On putting the value we get ,
\[ = \dfrac{{18}}{{96}} \times 100\]
On solving we get ,
\[ = 18.75\% \]
So, the correct answer is “18.75 %”.

Note: In the questions related to the cost price or selling price always , let assume a variable which is equal to the actual value or required value of the object . Profit or loss is always calculated on the cost price of the product or article. Selling price greater than cost price results in profit and vice versa results in loss.