Question

Each book on a certain shelf is labeled by a single category. For every 2 history books, there are 7 fantasy books and for every 3 fantasy books, there are 5 reference books. If the proportion of history to reference books is doubled, while the proportion of fantasy to reference books is maintained, which of the following could be the number of history books if there are fewer than 60 fantasy books on the shelf after the changes?A. 6

B. 21
C. 24
D. 35
E. 36

Answer 1

240

Explanation:

Given that each book on a certain shelf is labeled by a single category. For every 2 history books, there are 7 fantasy books and for every 3 fantasy books, there are 5 reference books

Let history, fantasy and reference books be x,y,z

Then x:y =2:7, y:z = 3:5

Or x:y:z =6:21:35

Now when we double x:y we get

x:y = 4:7 while y:z=3:5

we get

x:y:z = 12:21:35

Original fantasy books =
`(21)/(62)`

New fantasy books =
`(21)/(68)`

Difference = 0.3387-0.3088

=0.299

Approxly 3 is differene equivalent to 60

So new X =
`60*12/3\\=240`