Each of the 75 workers of a factory comes to work by bus or by train or both. If 48 workers come by bus and 41 come by train, how many workers use both the bus and the train?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 14
Every worker uses at least one of the two, so the workers who come by bus or train number 75 in all. Those who use both are counted twice when the two numbers are added: \(n(A\text{ or }B)=n(A)+n(B)-n(\text{both})\).
\(75=48+41-n(\text{both})\)
\(n(\text{both})=89-75=14\)
Check: bus only \(=48-14=34\), train only \(=41-14=27\), and \(34+14+27=75\)
Checking the other options
Option (1): 34 — Incorrect. This is the number who use the bus only.
Option (2): 27 — Incorrect. This is the number who use the train only.
Option (3): 89 — Incorrect. This is 48 + 41, which counts the workers who use both twice; it is more than the 75 workers.