What marks did Abhijit score in English? I. Marks in Mathematics exceed marks in Science by 20. II. Total marks in Mathematics, Science, English = 197. III. Marks in Science exceed marks in English by 12.

Difficulty: Medium

Correct Answer: I, II and III

Explanation:


Introduction / Context:
We must uniquely determine the English score using linear relations among three subjects.



Step-by-Step Solution:

  • Let E = English, S = Science, M = Math.
  • I: M = S + 20.
  • II: M + S + E = 197.
  • III: S = E + 12.

Substitute III into I ⇒ M = (E + 12) + 20 = E + 32.Use II: (E + 32) + (E + 12) + E = 197 ⇒ 3E + 44 = 197 ⇒ E = 51.



Sufficiency Check:
Any two statements leave one degree of freedom; all three are needed for a unique E.



Final Answer:
I, II and III.

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