The ratio of textbooks to novels to atlases in a certain classroom is 2 to 4 to 3. If there are no other books in the classroom, and if the teacher adds textbooks until novels make up 32% of the books present, which of the following could be the number of atlases in the room?

A. 9

B. 16

C. 34

D. 51

E. 78

Textbook = T, Novel = N, Atlas = A.

T:N:A = 2:4:3

Currently percentage of N = 4/(4+2+3) = 4/9 = 44.44%

T is added until N becomes 32% or we can say

if 100 is the new total number of books 32 of them is N

or if 50 is the new total number of books 16 of them is N

or if 25 is the new total number of books 8 of them is N

So, we see that N should be a multiple of 8.

There is no change in the number of Atlas, hence as per its ratio, Atlas should be a multiple of 3.

B and C are out.

Work back from answers:

A. 9

If Atlas is 9, N will be 12 (not multiple of 8). Out. [as ratio of T:N:A is 2:4:3]

D. 51

If Atlas is 51, N will be 68 (not multiple of 8). Out.

E. 78

If Atlas is 78, N will be 104 (multiple of 8). Hence, the answer.We can also see that if N = 104, T=52 and A=78, T:N:A = 2:4:3

If 91 more T are added, % of N = 104/325=32%

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