IMO B.

This question is basically trying to confuse & consume time if you don't interpret the data properly.

We can either choose to select numbers or use variables. I prefer chosing numbers because using variables can sometimes get confusing especially when running against time.

The question says there are twice english majors as history majors & then goes on to say there are three times english majors as mathematics majors.

English majors are common in the comparison, we have to keep that as our reference & chose numbers for history & mathematics majors.

Lets assume there are 30 English majors. From the info provided in the question, history majors will be 15 & mathematics majors will be 10. From this ratio of the number of history majors to mathematics majors ==> 15/10 ==> 3 : 2
---------------------------------------------------------------------------------
We can use the variables, lets assume H, E & M as the variables for History, English & Mathematics.

2H = E & 3M = E ==> H = E/2 & M = E/3.

So, H/M ==> (E/2)/(E/3) ==> 3 : 2

Hope this helps.

Lets assume number of histoy major = x
therefore, English major would be 2x

Math Major = 1/3rd of english major = 2x/3

history major: Math major = x/(2x/3) = x * (3/2x)
= 3:2

B