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Explanation:

Let there be a, b and c questions in groups A, B and C respectively.

Then, a + b + c =100

Total marks = a + 2b + 3c

Also, aa+2b+3c60100

b = 23

⇒ a + c = 77

⇒ a = 77 – c

aa+46+3c0.6

⇒ a ≥ 0.6a + 27.6 + 1.8c

⇒ 4a ≥ 276 + 18c

⇒ a ≥ 69 + 4.5c

⇒ a – 4.5c ≥ 69

⇒ 77 – c – 4.5c ≥ 69

⇒ 77 ≥ 69 + 5.5c

⇒ c ≤ 8/5.5

⇒ c = 1

Hence, option (a).

Alternatively,
Evaluating options,

If C has 1 question then B and A have 23 and 76 questions respectively.
The total number of marks = 125
⇒ Group A has 60.8% marks.
⇒ Option (a) is possible.

If C has 2 questions then B and A have 23 and 75 questions respectively.
The total number of marks = 127
⇒ Group A has 59.05% marks.
⇒ Option (b) is not possible.

If C has 3 questions then B and A have 23 and 74 questions respectively.
The total number of marks = 129
⇒ Group A has 57.36% marks.
⇒ Option (c) is not possible.

Hence, option (a).

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