Question

An uneducated retailer marks all his goods at 50% above the cost price and thinking that he will still make 25% profit, offers a discount of 25% of the marked price. What is the actual profit on the sales?
A. 11%
B. 12%
C. 12.50%
D. 13.50%

Answer 1

Hint: Cost price is the amount paid by seller to acquire product and marked price (selling price) is the price acquired by seller after selling the product to customer.
Mark Price: selling price' is the amount you actually pay for the thing when you purchase. 'marked price' is the general price of the thing without any discount. 'discount' is a percentage of the marked price.
Profit and Loss: is considered as the gain amount from any business activity. Whenever a shopkeeper sells a product, his motive is to gain some benefit from the buyer in the name of profit. Basically, when he sells the product more than its cost price, then he gets the profit on it but if he has to sell it for less than its cost price, then he has to suffer the loss.
\[\begin{gathered}
  Profit = Marked\,Price - \operatorname{Cos} t\,price \\
  Loss = \,\operatorname{Cos} t\,Price - Marked\, Price \\
  Profit\% = \dfrac{{profit}}{{\cos t\,price}} \times 100 \\
\end{gathered} \]
Similarly, loss.

Complete step by step solution:
Let Amount of product be x
Since seller sells the product at 50% of cost price
Marked price will be
\[\begin{gathered}
   = (x + x \times 50\% ) \\
   = x + x \times \dfrac{{50}}{{100}} \\
   = x + 0.5x \\
   = 1.5x \\
\end{gathered} \]
Now the shopkeeper sells this product with a discount of 25% on marked price.
Therefore
Selling price
\[\begin{gathered}
   = (1.5x - 1.5x \times \dfrac{{25}}{{100}}) \\
   = 1.5x \times 0.75 \\
   = 1.125x \\
\end{gathered} \]
Total profit we made is
\[(Selling)\, Price - \operatorname{Cost}\,Price)\]
\[\begin{gathered}
  Profit = (1.125x - x) \\
  \,\,\,\,\,\,\,\,\,\,\,\,\,\, = 0.125x \\
  Profit\% = 0.125x \times \dfrac{{100}}{x} \\
  \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 12.5\% \\
\end{gathered} \]

Thus, option C is the correct answer.

Note:
Let cost price \[ = 100\,Rs\] then marked price \[ = 150\,Rs\]
Selling price \[ = 75\% \,of\,150\]
\[ \Rightarrow \dfrac{{75}}{{100}} \times 150 = 112.5\,Rs\]
Actual
\[\begin{gathered}
  Profit\% = \dfrac{{112.5 - 100}}{{100}} \times 100 \\
  \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 12.5\% \\
\end{gathered} \]