In this task, you need to provide the correct option for a given problem from the provided options.

Problem: if both 5 ^ 2 and 3 ^ 3 are factors of n x ( 2 ^ 5 ) x ( 12 ^ 2 ) x ( 7 ^ 3 ) x ( 10 ) , what is the smallest possible positive value of n ? 
Options: a ) 15 , b ) 45 , c ) 75 , d ) 125 , e ) 150
a

Problem: the ratio between the sale price and the cost price of an article is 6 : 5 . what is the ratio between the profit and the cost price of that article ? 
Options: a ) 2 : 9 , b ) 1 : 5 , c ) 3 : 6 , d ) 2 : 0 , e ) 2 : 1
b

Problem: a bottle contains a certain solution . in the bottled solution , the ratio of water to soap is 3 : 5 , and the ratio of soap to salt is four times this ratio . the solution is poured into an open container , and after some time , the ratio of water to soap in the open container is quartered by water evaporation . at that time , what is the ratio of water to salt in the solution ? 
Options: a ) 9 : 100 , b ) 100 : 9 , c ) 12 : 100 , d ) 12 : 20 , e ) 13 : 100

a