Hello,

Can you please assist with this:

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?


Answer choices:

6
21
24
35
36

OA: 24


My solution was as follows:

H : F : R
2 : 7
3 : 5

So,

H : F : R
6 : 21
21: 35


However, I was stuck after this point. I was not clear with the following:

If the proportion of history to reference books is doubled, while the proportion of fantasy to reference books is maintained

The official explanation states:

The proportion of history to reference books is doubled but the proportion of fantasy to reference books is unchanged. Don't change the fantasy or reference numbers. Double the history component from 6 to 12. The new ratio is:
H:F:R = 12:21:35

I was not sure why we double the history books and not the reference books.

Thanks for your help - Sri