Question

How much percent above the cost price should a shopkeeper mark his goods so that after allowing a discount of 20% on the marked price, he gains 12%.

Answer 1

Hint: First of all, let the cost price be Rs100. Now, calculate the profit on Rs100 and then add it to the cost price and you will get the selling price. Now, let the marked price be x. And the shopkeeper gives a discount of 20% so the selling price would be 80% of x. Now compare both the selling prices and you will get the marked price.

Complete step-by-step answer:
In this question, we are asked how much percent above the cost price should a shopkeeper mark his goods so that after giving 20% discount on the market price he gains 12% profit.
Let the Cost price be Rs100
 $ \Rightarrow C.P = Rs100 $
Now, the shopkeeper is earning a profit of 12%.
So the profit earned in Rs will be
 $ \Rightarrow \Pr ofit = \dfrac{{12}}{{100}} \times 100 = Rs12 $
Now, the selling price is given by cost price plus the profit. Therefore,
 $ \Rightarrow S.P = C.P + \Pr ofit $
  $ = 100 + 12 $
 $ \Rightarrow S.P = 112 $ - - - - - - - - - (1)
Now, let the marked price be Rs x and the shopkeeper is providing a discount of 20%. So the selling price will be 80% of Rs x.
 $ \Rightarrow S.P = 80\% $ of x
 $ \Rightarrow S.P = \dfrac{{80}}{{100}} \times x $ - - - - - - - - - - (2)
Therefore, from equation (1) and (2), we get
 $
   \Rightarrow \dfrac{{80}}{{100}} \times x = 112 \\
   \Rightarrow x = \dfrac{{112 \times 100}}{{80}} \\
   \Rightarrow x = 140 \;
  $
Hence, the marked price will be 40% above the CP.
So, the correct answer is “40%”.

Note: Here, note that the value we obtained for x that is 140 is the marked price the shopkeeper is going to use. But we are supposed to find how much percent of the market price should be above the cost price to gain profit. So, here we had taken the cost price 100. So, we can see that the market price is Rs40 higher than the cost price. Hence, on converting Rs40 into percent, we get 40%