Question

A retailer marks his goods at a
price that he would get a profit of 40%. He sold 40% of the goods at this
price, half of the remainings at a discount of 20% and the rest at two sucessive
discounts of 20% each. Find his loss percent or profit percent on the whole.

Answer 1

MP marked price = (140/100) * CP  as  then profit is  (MP - CP) / CP = 40%
Let there be N number of goods or items. 
Money earned from 40% of the goods = MP * number of goods sold
     = MP * (40/100 * N) =  1.40 CP * 0.40 N = 0.56 N CP

half of the remaining goods = 1/2 of 60% remaining = 1/2 * 60/100 * N = 0.30 N
THese are sold at 20% discount.
Their sale price =  MP (100 - discount)/100 = 1.40 CP 80/100 = 1.12 CP
Money earned from their sale = 1.12 CP * 0.30 N = 0.336 CP * N

Half of the remaining goods (at this point 30% are left after selling 40% & 30 % earlier)
   = 15% = 0.15 N
their selling price = 40% discount from MP    increase of 20% more discount than previous set of goods.  The selling price =  (100 - 40)/100 MP = 0.60 * 1.40 CP = 0.84 CP
Money received from their sale = 0.84 CP * 0.15 N = 0.1260 CP N

the last set of goods = 15 % = 0.15 N
their selling price =  60 % discount from MP = (100 - 60)/100 * MP = 0.40* 1.40 CP
     = 0.56 CP
money received from their sales =  0.56 CP * 0.15 N =  0.0840 CP N

Total money received fom sales = ( 0.56 +0.336 + 0.126 + 0.084 ) CP * N
           = 1.106 CP * N
Total profit earned = 1.106 -  CP * N  = 0.106 N CP
Profit % earned = 100  * 0.106 N CP / N CP = 0.106 * 100 = 10.6 %