Question

A dealer marks his goods at 35% above the cost price and allows a discount of 20% on the market price. Find his gain or loss percent.

Answer 1

Hint: In this question, we need to evaluate the gain or the loss percent incurred by the dealer while selling the product at a discount of 20% on the market price while marking the price of the product at 35% above the cost price. For this, we will first calculate the cost price and the selling price of the product and then, eventually determine the percentage.

Complete step-by-step answer:
Let the cost price, marked price and the selling price of the product for the dealer be CP, MP and SP respectively.
According to the question, the marked price of the product is 35% more than the cost price of the product for the dealer.
So,
 $
  MP = CP + 35\% \;of\;CP \\
   = CP + 0.35CP \\
   = 1.35CP - - - - (i) \;
  $
Also, it has been given in the question that the selling price of the product is after allowing a discount of 20% on the marked price of the product. So,
 $
\Rightarrow SP = 1.35CP - 20\% \;of\;(1.35CP) \\
   = 1.35CP - 0.2 \times 1.35CP \\
   = 0.8 \times 1.35CP \\
   = 1.08CP - - - - (ii) \;
  $
From equation (i) and (ii), we can see that the selling price of the product is more than the cost price of the product. So, dealers will gain profit on selling the product.
Now, the difference between the selling price and the cost price is the profit on the product. So,
 $
\Rightarrow Gain = SP - CP \\
   = 1.08CP - CP \\
   = 0.8CP \;
  $
Now, for the gain percentage,
 $
\Rightarrow Gain\% = \dfrac{{Gain}}{{CP}} \times 100 \\
   = \dfrac{{0.8CP}}{{CP}} \times 100 \\
   = 80\% \;
  $
Hence, the gain percentage on selling the product is 80%.
So, the correct answer is “ 80%”.

Note: It is interesting to note here that, the selling price and the marked price of the product both depend on the cost price of the product. Also, the gain percentage or the loss percentage of the product depends on the cost price of the product as well. So, we need to always stick with only one parameter in this question i.e., the cost price of the product.