A student was asked to multiply a positive number \(N\) by \(\displaystyle\frac{4}{5}\), but instead he divided \(N\) by \(\displaystyle\frac{4}{5}\). The two answers differ by 36. What is the value of \(N\)?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 80
Dividing by \(\displaystyle\frac{4}{5}\) is the same as multiplying by \(\displaystyle\frac{5}{4}\), so the wrong answer is \(\displaystyle\frac{5 N}{4}\) and the correct one is \(\displaystyle\frac{4 N}{5}\).
\(\displaystyle\frac{5 N}{4}-\frac{4 N}{5}=\frac{25 N-16 N}{20}=\frac{9 N}{20}\)
\(\displaystyle\frac{9 N}{20}=36\)
\(N=\displaystyle\frac{36\times20}{9}=80\)
Check: \(\displaystyle\frac{5}{4}\times80=100\) and \(\displaystyle\frac{4}{5}\times80=64\), and \(100-64=36\). The value of \(N\) is 80.
Why the other options are incorrect
Option (1) 100 — Incorrect. For \(N=100\): \(\displaystyle\frac{5}{4}\times100=125\) and \(\displaystyle\frac{4}{5}\times100=80\), which differ by 45, not 36.
Option (3) 45 — Incorrect. For \(N=45\): \(\displaystyle\frac{5}{4}\times45=56.25\) and \(\displaystyle\frac{4}{5}\times45=36\), which differ by 20.25, not 36.
Option (4) 60 — Incorrect. For \(N=60\): \(\displaystyle\frac{5}{4}\times60=75\) and \(\displaystyle\frac{4}{5}\times60=48\), which differ by 27, not 36.