An important proof

Let
 Cost Price=cp
Selling price=sp
Case-I
If we sell one thing on x% gain then 
sp1=[(100+x)*cp]/100
 and  now the purchaser  of this thing  sells it on  x% loss 
then  sp2=[(100+x)*cp]/100-[(100+x)*cp*x]/(100*100 )
where   [(100+x)*cp*x]/(100*100 )=x% of sp1(i.e loss)
or sp2=[{(100+x)*cp}/100][1-x/100]
now  net  loss or gain=cp-sp2= -(x*x*cp)/(100*100)


(-)ve sign tells that we  incur loss
     so  net loss %=[(cp-sp2)*100]/cp= (x*x)/( 10*10)

Case-II
 If we sell one thing on x% loss and then 
 purchaser  of this thing  sells it on  x% gain
then from same process of  Case-I 

   net loss % =(x*x) / 10*10

Example:
If  actual cost of a thing is cp.and we purchase it from seller by giving him x% loss.Then selling price for that seller is sp and this sp is cp for us.now we sell it on gain of x% of this cp.Then we incur gain but the thing always  incurs  loss of  (x*x)/(10*10)
Reverse
If  actual cost of a thing is cp.and we purchase it from seller by giving him x% gain.Then selling price for that seller is sp and this sp is cp for us.now we sell it on loss of x% of this cp.Then we incur loss but the thing also always  incurs  loss of  (x*x)/(10*10)