A student was asked to multiply a positive number \(N\) by \(\displaystyle\frac{3}{5}\), but instead he divided \(N\) by \(\displaystyle\frac{3}{5}\). The two answers differ by 48. What is the value of \(N\)?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 45
Dividing by \(\displaystyle\frac{3}{5}\) is the same as multiplying by \(\displaystyle\frac{5}{3}\), so the wrong answer is \(\displaystyle\frac{5 N}{3}\) and the correct one is \(\displaystyle\frac{3 N}{5}\).
\(\displaystyle\frac{5 N}{3}-\frac{3 N}{5}=\frac{25 N-9 N}{15}=\frac{16 N}{15}\)
\(\displaystyle\frac{16 N}{15}=48\)
\(N=\displaystyle\frac{48\times15}{16}=45\)
Check: \(\displaystyle\frac{5}{3}\times45=75\) and \(\displaystyle\frac{3}{5}\times45=27\), and \(75-27=48\). The value of \(N\) is 45.
Why the other options are incorrect
Option (1) 30 — Incorrect. For \(N=30\): \(\displaystyle\frac{5}{3}\times30=50\) and \(\displaystyle\frac{3}{5}\times30=18\), which differ by 32, not 48.
Option (3) 60 — Incorrect. For \(N=60\): \(\displaystyle\frac{5}{3}\times60=100\) and \(\displaystyle\frac{3}{5}\times60=36\), which differ by 64, not 48.
Option (4) 36 — Incorrect. For \(N=36\): \(\displaystyle\frac{5}{3}\times36=60\) and \(\displaystyle\frac{3}{5}\times36=21.6\), which differ by 38.4, not 48.