The public library has exactly 2 floors. It has 2/3 as many shelves on its 2nd floor as it does on its 1st. If the second floor has 1/6 as many books per shelf as the first floor, what fraction of the library's books are on the first floor? Choose the correct choice from the following options.
A) 1/4  B) 9/10  C) 5/9  D) 9/14  E) 5/6
Let x be the no of shelves and y be the no of books per shelf on first floor.   Now no of shelves on 2nd floor = (2/3)*x   no of books per shelf on 2nd floor = (1/6) * y   So total no books on first floor = xy and total no of books on 2nd floor = (2/3)*x*(1/6)*y = (1/9)*xy   fraction of library books on first floor = (xy)/(xy + (1/9)*xy)   =1 / (1+(1/9))   =9/10   So 9/10
<result>B</result>
The public library has exactly 2 floors. It has 2/3 as many shelves on its 2nd floor as it does on its 1st. If the second floor has 1/6 as many books per shelf as the first floor, what fraction of the library's books are on the first floor?