Question

A trader gives 25% discount
on his articles and still makes a profit of 25%. Find his profit percent, if he
sells his articles at:

(i) 10% discount (ii) their marked price

Answer 1

Cost price = CP
Marked price = MP  This is the price marked on items. Discount is given on this price
Sale price after discount SP = MP * (100 - discount%)/100
Profit = SP - CP = MP*(100-discount%)/100  -   CP
Profit % = profit * 100 / CP  =  MP(100-discount%)/CP -  100

  profit %=     25 = MP (100-25)/CP  - 100    =>  125 = MP 75 / CP
              =>  MP = 5/3 CP
  Formula for profit % = 5/3 *CP (100-discount%) / CP  - 100
                               =  5/3 (100 - discount%) - 100

1)  Discount = 10%  So  profit %  =  5/3 * (100 -10) - 100  = 50%
2 )  SP = MP =>  discount is zero% 
             profit % = 5/3 (100 - 0) - 100  = 66.66%