A civil services training cohort has 60 officers. 36 speak Pashto, 28 speak Balochi, and 12 speak neither language. How many officers speak both Pashto and Balochi?
Answer and explanation
Correct answer: D. 16 officers
- Step 1: Officers who speak at least one language = 60 - 12 = 48 officers.
- Step 2: By principle of inclusion-exclusion: n(P ∪ B) = n(P) + n(B) - n(P ∩ B).
- Step 3: 48 = 36 + 28 - n(P ∩ B) = 64 - n(P ∩ B).
- Step 4: n(P ∩ B) = 64 - 48 = 16 officers.
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