Question

A dealer marked his goods 20% above the cost price and allowed a discount of 10%. Then, the gain percent is
A. 2%
B. 4%
C. 6%
D. 8%

Answer 1

Hint: Let the cost price (CP) of the goods is x. Then the marked price of the goods will be $ x + 20\% ofx = x + 0.2x = 1.2x $ and the discount is 10%. The discount price is 10% of 1.2x. Selling price (SP) is marked price minus discount price. Then substitute the values of SP and CP in the below formula to get the profit percentage.
 $ Profit = \dfrac{{\left( {SP - CP} \right)}}{{CP}} \times 100 $ , where SP is the selling price and CP is the cost price.

Complete step-by-step answer:
We are given that a dealer marked his goods 20% above the cost price and allows a discount of 10%.
We have to find the gain percentage.
Let the cost price (CP) of the goods be x.
The marked price of the goods is 20% more than the cost price, this means marked price will be $ MP = x + 20\% ofx = x + \dfrac{{20}}{{100}}x = x + 0.2x = 1.2x $
The marked price (MP) is 1.2x.
The discount is 10%. The price of discount is
 $
  D = 10\% of1.2x = \dfrac{{10}}{{100}} \times 1.2x \\
   \Rightarrow D = 0.1 \times 1.2x \\
  D = 0.12x \\
  $
The selling price is marked price minus the discount price, $ MP - D $
 $ SP = 1.2x - 0.12x = 1.08x $
Profit percentage can be found using $ Profit = \dfrac{{\left( {SP - CP} \right)}}{{CP}} \times 100 $
 $
  SP = 1.08x,CP = x \\
   \Rightarrow Profit = \dfrac{{\left( {1.08x - x} \right)}}{x} \times 100 \\
   \Rightarrow Profit = \dfrac{{0.08x}}{x} \times 100 = 0.08 \times 100 \\
  \therefore Profit = 8\% \\
  $
The gain percent is 8%.

So, the correct answer is “Option D”.

Note: Cost price is the price at which an item is purchased and the selling price is the price at which that item is sold. The price which is marked as the selling price without the discount is known as marked price. The actual selling price will be marked price minus discount price, when there is any discount. If there is no discount then the marked price is the actual selling price.