\(\mathrm{P}\) is directly proportional to \(\mathrm{M}\) and inversely proportional to \(\mathrm{N}\). If \(\mathrm{P}=9\) when \(\mathrm{M}=24\) and \(\mathrm{N}\) \(=8\), find the value of \(P\) when \(M=5\) and \(N=6\)
A. \(1 \frac{1}{4}\) B. \(2 \frac{1}{2}\) C. \(3 \frac{3}{5}\) D. 11
Correct Answer: B
Explanation
\(\mathrm{P} \alpha \frac{\mathrm{M}}{\mathrm{N}}, \mathrm{P}=\frac{\mathrm{KM}}{\mathrm{N}}, \mathrm{K}=\frac{\mathrm{PN}}{\mathrm{M}}\) \(\mathrm{K}=\frac{9 \times 8}{24}=\frac{72}{24}=3\) Then, when \(\mathrm{M}=5\) and \(\mathrm{N}=6\), we have: \(3=\frac{\mathrm{P} \times 6}{5}, \mathrm{P}=\frac{3 \times 5}{6}=\frac{5}{2}=2 \frac{1}{2}\)