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 = 8/5
A.
12(8/5)
B.
15
C.
10
D.
28(8/5)
Correct Answer: 10
Explanation
P ∝ mu, p ∝1/q
p = muk ................ (1)
p = 1/qk... (2)
Combining (1) and (2), we get
P = (mu/q)k
4 = (m × u/1)k
giving k = 4/6 = 2/3
So, P = mu/q × 2/3 =(2mu/3q)
Hence, P = (2 × 6 × 4)/(3 ×8/5)
P = (2 × 6 × 4 × 5/3 × 8)
p = 10
P ∝ mu, p ∝1/q
p = muk ................ (1)
p = 1/qk... (2)
Combining (1) and (2), we get
P = (mu/q)k
4 = (m × u/1)k
giving k = 4/6 = 2/3
So, P = mu/q × 2/3 =(2mu/3q)
Hence, P = (2 × 6 × 4)/(3 ×8/5)
P = (2 × 6 × 4 × 5/3 × 8)
p = 10
