Let E be the number of English books and C be the number of Chinese books.

Let S be the number of the second hand books and N be the number of new books.


Then   =  = 4, since  "80 percent of the books in a box are 2nd hand books and the rest are new."

In other words,  S = 4N.     (1)


Next, the condition says that

0.1*N + 0.6*S = E       (2)   ("10 percent of the new and 60 percent of the 2nd hand are english")   and

0.9*N + 0.4*S = C       (3)   ("the rest are chinese")


Now, substitute (1) into (2) and (3). You will get

0.1*N + 0.6*(4N) = E    (2')

0.9*N + 0.4*(4N) = C    (3')

or, simplifying


2.5*N = E                (2'')

2.5*N = C                (3'')


Thus  E = C   (!!!).


Next, use the last condition  

 = ,

which (due to (!!!) ) is the same as

 = .


It implies  2*(E+15) = 3E,   or  2E + 30 = 3E  ====>  E = 30.


Thus the number of English books initially was 30.  


Then the total number of the books at the end is  E + C + 15 = E + E + 15 = 75.