In a group of 48 teachers, 27 can speak Tamil, 22 can speak Telugu and 9 can speak both languages. How many teachers can speak neither of the two languages?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 8
The teachers who speak both languages are counted once among the Tamil speakers and once among the Telugu speakers, so they are subtracted once: \(n(A\text{ or }B)=n(A)+n(B)-n(\text{both})\).
Tamil only \(=27-9=18\)
Telugu only \(=22-9=13\)
Tamil or Telugu (or both) \(=27+22-9=40\)
Neither \(=48-40=8\)
Checking the other options
Option (1): 40 — Incorrect. This is the number who can speak at least one of the two languages, not neither.
Option (3): 18 — Incorrect. This is the number who speak Tamil only.
Option (4): 13 — Incorrect. This is the number who speak Telugu only.