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There are six teachers 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 is 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 reverse of those of D's. Chemistry is an optional subject of any one of them. There is only one female teacher in the school who has English as her compulsory subject.
Q. Which of the following groups of teachers has History as the compulsory subject?
  • a)
    A, C and D
  • b)
    B, C and D
  • c)
    C and D
  • d)
    A, B and C
Correct answer is option 'D'. Can you explain this answer?
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There are six teachersA, B, C, D, EandFin a school. Each of the teache...
A, B and C have History as the compulsory subjects
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There are six teachersA, B, C, D, EandFin a school. Each of the teache...
Solution:

Given information:

- There are six teachers A, B, C, D, E, and F.
- Each teacher teaches two subjects - one compulsory and one optional.
- D's optional subject is History.
- Three teachers have History as their 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 reverse of those of D.
- Chemistry is an optional subject of any one of them.
- There is only one female teacher in the school who has English as her compulsory subject.

To find: The group of teachers who have History as their compulsory subject.

Solution:

From the given information, we can make the following table:

| Teacher | Compulsory Subject | Optional Subject |
|---------|-------------------|------------------|
| A | English | History |
| B | | |
| C | | |
| D | History | |
| E | | |
| F | Mathematics | Physics |

- D has History as an optional subject. Therefore, D's compulsory subject is not History.
- Three teachers have History as their compulsory subject. Therefore, the remaining three teachers must have History as their optional subject.
- E and F have Physics as one of their subjects. Therefore, A, B, C, and D must have Physics as their optional subject.
- F's compulsory subject is Mathematics which is an optional subject of both C and E. Therefore, neither of C or E can have Mathematics as their compulsory subject.
- History and English are A's subjects but in terms of compulsory and optional subjects, they are reverse of those of D. Therefore, A's compulsory subject is not History.
- Chemistry is an optional subject of any one of them. Therefore, we cannot determine which teacher has Chemistry as an optional subject.

Using the above deductions, we can fill in the table as follows:

| Teacher | Compulsory Subject | Optional Subject |
|---------|-------------------|------------------|
| A | English | History |
| B | Physics | History |
| C | Physics | History |
| D | | History |
| E | Physics | History |
| F | Mathematics | Physics |

- D's compulsory subject is Physics.
- Therefore, the group of teachers who have History as their compulsory subject is A, B, and C.

Hence, the correct option is D.
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Community Answer
There are six teachersA, B, C, D, EandFin a school. Each of the teache...
D
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