Question

How much percent above the cost prize should a shopkeeper mark his goods so that even after allowing a discount of 20%, he still gains 10%?

Answer 1

Let the shopkeeper mark the prices at  x% higher than cost price CP.
Let MP = (100+x)/100 * CP 

Price after discount = 80% MP = 80(100+x) CP /10,000
sale price with a gain of 10% = 110 % CP 

Hence :  110 CP/100 = 80 (100+x) CP / 10, 000 
 
          100 +x = 110 * 100 / 80 = 137.5 
 
      x = 37.5   =>   Marking price is 37.5 % above cost price.

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alternately

let the cost price be Rs 100.

MP = 100 + x 

Price after discount = (100 + x) * 80/100 
Sale price with 10% gain =  CP + 10% CP = 100 + 10 = Rs 110

Hence (100 + x) 8/10 = 110    =>  100 + x = 1100/8 = 137.5 

x = 37.5 %