A student was asked to multiply a positive number \(N\) by \(\displaystyle\frac{5}{6}\), but instead he divided \(N\) by \(\displaystyle\frac{5}{6}\). The two answers differ by 22. What is the value of \(N\)?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 60
Dividing by \(\displaystyle\frac{5}{6}\) is the same as multiplying by \(\displaystyle\frac{6}{5}\), so the wrong answer is \(\displaystyle\frac{6 N}{5}\) and the correct one is \(\displaystyle\frac{5 N}{6}\).
\(\displaystyle\frac{6 N}{5}-\frac{5 N}{6}=\frac{36 N-25 N}{30}=\frac{11 N}{30}\)
\(\displaystyle\frac{11 N}{30}=22\)
\(N=\displaystyle\frac{22\times30}{11}=60\)
Check: \(\displaystyle\frac{6}{5}\times60=72\) and \(\displaystyle\frac{5}{6}\times60=50\), and \(72-50=22\). The value of \(N\) is 60.
Why the other options are incorrect
Option (1) 30 — Incorrect. For \(N=30\): \(\displaystyle\frac{6}{5}\times30=36\) and \(\displaystyle\frac{5}{6}\times30=25\), which differ by 11, not 22.
Option (3) 66 — Incorrect. For \(N=66\): \(\displaystyle\frac{6}{5}\times66=79.2\) and \(\displaystyle\frac{5}{6}\times66=55\), which differ by 24.2, not 22.
Option (4) 48 — Incorrect. For \(N=48\): \(\displaystyle\frac{6}{5}\times48=57.6\) and \(\displaystyle\frac{5}{6}\times48=40\), which differ by 17.6, not 22.