There are six persons A, B, C, D, E and F in a school. Each of the teachers teaches two subjects, one compulsory subject and the other optional subject. D's optional subject was History while three others have it as compulsory subject. E and F have Physics as one of their subjects. F's compulsory subject is Mathematics which is an optional subject of both C and E. History and English are A's subjects but in terms of compulsory and optional subjects, they are just reverse of those of D's. Chemistry is an optional subject of only one of them. The only female teacher in the school has English as her compulsory subject.

Disregarding which is the compulsory and which is the optional subject, who has the same two subject combination as F ?

A. A
B. B
C. E
D. D
E. None of these
Answer: C . E


The given information can be analysed as follows :
Let 'O' denote optional and 'C' denote compulsory .

  A B C D E F
History C C C O - -
Physics - - - - C O
Mathematics - - O - O C
English O - - C - -
Chemistry - O - - - -

One compulsory subject of F is Mathematic. F has Physics as one of the subjects. So, Physics is optional of F. F has Mathematics as optional and Physics as one subject.
So, Physics is the compulsory subject of E. A and D have the same subjects -- History and English. D has History as optional subject and so English is the compulsory subject of D. Subjects of A and D are reverse in regard of optional and compulsory.
So, A has History as compulsory subject and English as optional.
Chemistry is the optional subject of only one teacher. So, it is the optional of B, which only remains.
We know that History is the compulsory subject of three teachers. So, it is compulsory for A, B and C.
D is the teacher having English as her compulsory subject.
So, D is the only female teacher.

Clearly, E has the same subject combination as that of F.