A student was asked to multiply a positive number \(N\) by \(\displaystyle\frac{3}{4}\), but instead he divided \(N\) by \(\displaystyle\frac{3}{4}\). The two answers differ by 14. What is the value of \(N\)?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 24
Dividing by \(\displaystyle\frac{3}{4}\) is the same as multiplying by \(\displaystyle\frac{4}{3}\), so the wrong answer is \(\displaystyle\frac{4N}{3}\) and the correct one is \(\displaystyle\frac{3N}{4}\).
\(\displaystyle\frac{4N}{3}-\frac{3N}{4}=\frac{16N-9N}{12}=\frac{7N}{12}\)
\(\displaystyle\frac{7N}{12}=14\)
\(N=\displaystyle\frac{14\times12}{7}=24\)
Check: \(\displaystyle\frac{4}{3}\times24=32\) and \(\displaystyle\frac{3}{4}\times24=18\), and \(32-18=14\). The value of \(N\) is 24.