A student was asked to multiply a positive number \(N\) by \(\displaystyle\frac{2}{3}\), but instead he divided \(N\) by \(\displaystyle\frac{2}{3}\). The two answers differ by 25. What is the value of \(N\)?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 30
Dividing by \(\displaystyle\frac{2}{3}\) is the same as multiplying by \(\displaystyle\frac{3}{2}\), so the wrong answer is \(\displaystyle\frac{3 N}{2}\) and the correct one is \(\displaystyle\frac{2 N}{3}\).
\(\displaystyle\frac{3 N}{2}-\frac{2 N}{3}=\frac{9 N-4 N}{6}=\frac{5 N}{6}\)
\(\displaystyle\frac{5 N}{6}=25\)
\(N=\displaystyle\frac{25\times6}{5}=30\)
Check: \(\displaystyle\frac{3}{2}\times30=45\) and \(\displaystyle\frac{2}{3}\times30=20\), and \(45-20=25\). The value of \(N\) is 30.
Why the other options are incorrect
Option (2) 24 — Incorrect. For \(N=24\): \(\displaystyle\frac{3}{2}\times24=36\) and \(\displaystyle\frac{2}{3}\times24=16\), which differ by 20, not 25.
Option (3) 36 — Incorrect. For \(N=36\): \(\displaystyle\frac{3}{2}\times36=54\) and \(\displaystyle\frac{2}{3}\times36=24\), which differ by 30, not 25.
Option (4) 15 — Incorrect. For \(N=15\): \(\displaystyle\frac{3}{2}\times15=22.5\) and \(\displaystyle\frac{2}{3}\times15=10\), which differ by 12.5, not 25.