A town library has 6,400 members. The number of members goes up by 25% in one year and then comes down by 5% in the next year. How many members does the library have at the end of the two years?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 7600
The second change is a percentage of the number reached after the first change, not of the starting number.
After the first year: \(6400\times1.25=8000\)
After the second year: \(8000\times0.95=7600\)
The library has 7600 members at the end of two years.
Why the other options are incorrect
Option (1) 7680 — Incorrect. This takes a net change of \(25-5=20\%\) on 6,400; the 5% fall is on 8,000.
Option (3) 8000 — Incorrect. This is the number after the first year only.
Option (4) 7200 — Incorrect. This is \(8000\times0.90\), a 10% fall instead of 5%.