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Q18 (CAPF/2018) Science & Technology › Basic Science (Physics, Chemistry, Biology) › Quantitative aptitude topics Answer Verified

In an examination, 53% students passed in Mathematics, 61% passed in Physics, 60% passed in Chemistry, 24% passed in Mathematics and Physics, 35% in Physics and Chemistry, 27% in Mathematics and Chemistty' and 5% in none. The ratio of percentage of passes in Mathematics and Chemistry but not in Physics in relation to the percentage of passes in Physics and Chemistry but not in Mathematics is

Result
Your answer: —  Â·  Correct: B
Explanation

The correct answer is Option 2 (5:7). This problem is solved using the principles of set theory and Venn diagrams.

Let M, P, and C represent Mathematics, Physics, and Chemistry. Given:

  • Total students = 100%. Students who passed at least one subject = 100% - 5% (none) = 95%.
  • Using the formula: n(M∪P∪C) = n(M) + n(P) + n(C) - [n(M∩P) + n(P∩C) + n(M∩C)] + n(M∩P∩C).
  • 95 = 53 + 61 + 60 - [24 + 35 + 27] + n(M∩P∩C).
  • 95 = 174 - 86 + n(M∩P∩C) → 95 = 88 + n(M∩P∩C) → n(M∩P∩C) = 7%.

Now, calculate the required specific intersections:

  • Passes in M and C but not P: n(M∩C) - n(M∩P∩C) = 27% - 7% = 20%.
  • Passes in P and C but not M: n(P∩C) - n(M∩P∩C) = 35% - 7% = 28%.

The required ratio is 20:28, which simplifies to 5:7. Options 1, 3, and 4 are incorrect as they do not match this mathematical derivation.

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