P varies jointly as m and u, and varies inversely as q. Given that p = 4, m = 3 and u = 2 and q = 1, find the value of p when m = 6, u = 4 and q =\(\frac{8}{5}\)
A. 12\(\frac{8}{5}\) B. 15 C. 10 D. 28\(\frac{8}{5}\)
Correct Answer: C
Explanation
P \(\propto\) mu, p \(\propto \frac{1}{q}\) p = muk ................ (1) p = \(\frac{1}{q}k\).... (2) Combining (1) and (2), we get P = \(\frac{mu}{q}k\) 4 = \(\frac{m \times u}{1}k\) giving k = \(\frac{4}{6} = \frac{2}{3}\) So, P = \(\frac{mu}{q} \times \frac{2}{3} = \frac{2mu}{3q}\) Hence, P = \(\frac{2 \times 6 \times 4}{3 \times \frac{8}{5}}\) P = \(\frac{2 \times 6 \times 4 \times 5}{3 \times 8}\) p = 10