Let CP of object be a.  It is given that SP = $$(1+frac{4}{100} )$$ x CP  $$ Rightarrow $$ SP = 1.04 x CP
It is given that MP = $$(1+frac{x}{100} )$$ x CP It is also given that SP = $$(1-frac{frac {2x}{3}}{100} )$$ x MP  $$ Rightarrow $$ SP = $$(1-frac{2x}{300} )$$ x $$(1+frac{x}{100} )$$ x CP 
$$ Rightarrow (1+frac{4}{100})$$ x CP  = $$(1-frac{2x}{300} )$$ x $$(1+frac{x}{100} )$$ x CP 
$$ Rightarrow (1+frac{4}{100})$$   = $$(1-frac{2x}{300} )$$ x $$(1+frac{x}{100} )$$ 
$$ Rightarrow frac{104}{100}$$   = $$(1-frac{2x}{300} )$$ x $$(1+frac{x}{100} )$$ 
$$ Rightarrow frac{104}{100}$$   = $$(frac{300-2x}{300} )$$ x $$(frac{x+100}{100} )$$ 
$$ Rightarrow frac{104}{100} imes 300 imes 100$$   = $$(300-2x)$$ x $$(x+100)$$ 
$$ Rightarrow 31200 $$   = $$(300-2x)$$ x $$(x+100)$$ 
Now, we look at the options.  Since the question says that $$xepsilon[25,30]$$ so 50% of x ie 0.5x cannot be less than 12.50 ie $$frac {25}{2}$$ and cannot be more than 25 ie $$frac {50}{2}$$ This eliminates option A. Putting values of $$x$$ given in the remaining options in the final expression, [here we need to be careful to use the value of x and not the value of 50% of x as given in the expression] Look carefully in the remaining options : 16,13,15 as 0.5x ie 32,26,30 as possible values of x.  In the question since the discount rate offered is $$frac{2x}{3}$$%, then a safer choice would be to check for the option of 30 in the beginning. It is a safer choice because the percentage of discount that we get in the other options are not whole numbers.  NOTE : THIS IS JUST A SAFE CHOICE AND NEVER MARK AN ANSWER DIRECTLY ON THIS PRESUMPTION WITHOUT CHECKING IT. Putting x=30 in the expression :  (300 - (2x30))x(30+100) = (300-60)x(100+30) = 240x130 = 24x13x100= 312x100 = 31200= LHS of expression. Thus the value of $$x$$ is 30. Therefore value of 50% of $$x$$ = 0.5x30 = 15