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\(\frac{8}{5}\)
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
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
Source: Myschool Past Questions Archive (Record #27049)