Explanation
Let us break down the clues step-by-step to compile a comprehensive profile table for all 8 faculty members (A, B, C, D, E, F, G, H).
Step 1: Track Gender (3 Ladies, 5 Males)
From statement (vi): H and C are lady members.
From statement (vii): G is a lady member.
Since there are exactly 3 lady members altogether, the remaining five members (A, B, D, E, F) must be Male.
Step 2: Track Ph.D. Status (4 Ph.Ds, 4 Non-Ph.Ds)
From statement (iii): E is a Ph.D.
From statement (vi): F is a Ph.D., while H and C are not Ph.D.
From statement (vii): B and G are Ph.Ds.
Since we have found our 4 Ph.D. holders (B, E, F, G), the remaining members (A, D, C, H) must not hold a Ph.D.
Step 3: Map Subjects Using Given Statements
Let's populate a structural grid based on explicit statements:
E teaches Psychology (from statement iii).
A teaches Chemistry (from statement iii).
F teaches Zoology (from statement vi).
This leaves 5 subjects to distribute: Economics, Commerce, Law, Physics, and one remaining unnamed subject (let's call it Subject X).
Faculty | Gender | Ph.D. Status | Subject |
A | Male | No | Chemistry |
B | Male | Yes | |
C | Female | No | |
D | Male | No | |
E | Male | Yes | Psychology |
F | Male | Yes | Zoology |
G | Female | Yes | |
H | Female | No | |
Step 4: Eliminate Subjects and Find the Physics Faculty
Law Profile: Statement (iv) mentions "Law faculty does not award Ph.D.". Therefore, whoever teaches Law cannot be a Ph.D. holder.
Economics Profile: Statement (iv) states that the one who teaches Economics is not a Ph.D. holder.
Let's look at B and G:
Both B and G are Ph.D. holders. Therefore, neither can teach Law or Economics.
Statement (iv) states: "No lady member teaches either Commerce or Law". Since G is a lady, she cannot teach Commerce.
Statement (v) states: "D and G do not teach either Commerce or Physics".
Let's evaluate G's options:
G cannot teach: Chemistry, Psychology, Zoology (already taken).
G cannot teach: Law, Economics (since she is a Ph.D.).
G cannot teach: Commerce, Physics (explicitly stated in statement v).
Therefore, G must teach the 8th remaining subject (Subject X).
Let's evaluate B's options:
B cannot teach: Chemistry, Psychology, Zoology, Subject X (taken).
B cannot teach: Law, Economics (since he is a Ph.D.).
This leaves Commerce and Physics for B.
Since statement (v) says D cannot teach Commerce, and G is already assigned, let's look at who can teach Commerce and Law.
Lady members (C, G, H) cannot teach Commerce or Law. Since G is assigned, C and H definitely cannot teach Commerce or Law.
This means Commerce and Law must be taught by male faculties.
The available male faculties without subjects are B and D.
Since D cannot teach Commerce (statement v), B must teach Commerce.
Now let's find who teaches Physics:
The remaining unassigned subjects are Physics, Law, and Economics.
The remaining unassigned faculty members are C, D, and H.
Statement (v) states that D does not teach Physics.
Since D cannot teach Physics, and B is already teaching Commerce, the remaining slots for Physics must belong to either C or H.
There are no structural constraints left in the text to uniquely distinguish whether C teaches Physics and H teaches Economics/Law, or vice-versa.
Thus, Physics is taught by Either H or C.
Correct Answer
The correct option is (b) Either H or C.
