A museum lowers its entry fee by 25%, and as a result the number of visitors goes up by 40%. What happens to the museum’s collection from entry fees?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → It increases by 5%
Collection \(=\) fee \(\times\) number of visitors, so the two changes multiply.
New fee \(=0.75\) times the old fee
New number of visitors \(=1.40\) times the old number
New collection \(=0.75\times1.40=1.05\) times the old collection
Change \(=1.05-1=0.05=5\%\) increase
The collection increases by 5%.
Why the other options are incorrect
Option (2) It increases by 15% — Incorrect. This just adds \(40-25\); the changes multiply, and the cut also applies to the extra visitors: \(15-\frac{25\times40}{100}=5\).
Option (3) It decreases by 5% — Incorrect. \(1.05\) is more than 1, so the collection goes up, not down.
Option (4) It increases by 10% — Incorrect. That would need \(0.75\times1.40=1.10\), but the product is \(1.05\).