Solution
Understanding the set :-
This is a minima maxima + quantitative set :
Here you have 100 boxes and a mystery prices in every box, named as a, b, c...
Also, it is given that, there is price of item a is highest , then prices b, then price c, and so on...
Price a - a diamond ring is only in one of the box,
and other prices are atleast double in quantity of previous item i.e.,
we know item a is only 1 , then item b will be atleast two and item c will again be atleast double of item b.
Now, lets try to solve the set with the given information -
Option A: There are exactly 75 items of type e.
a=1,b=2,c=4,d=8, e=85.
Here the maximum value of e= 85.
Hence it can take the value 75.
An example of such case is a=1,b=2,c=4,d=18, e=75.
Option B: There are exactly 30 items of type b.
a=1 b=30 and c=69.
Hence this case is also possible.
Option C: There are exactly 45 items of type c.
Since the value of d should be at least 90, it means that d is not present because 45+90 will be more than 100(maximum number of items). Only a,b and c are present.
The maximum value of b = 22 and a =1, but 45+22+1=68, which is less than 100.
So this case is not possible.
Option D: There are exactly 60 items of type d.
d=60, c=30, b=9 and a=1. a+b+c+d=100.
Hence this case is possible.