P varies directly as Q and inversely as R. When Q = 36 and R = 16, P = 27. Find the relation between P, Q and R.

A.

\(P = \frac{Q}{12R}\)

B.

\(P = \frac{12Q}{R}\)

C.

\(P = 12QR\)

D.

\(P = \frac{12}{QR}\)

Correct answer is B

\(P \propto \frac{Q}{R}\)

\(P = K \frac{Q}{R}\)

When Q = 36, R = 16, P = 27

Then substitute into the equation

\(27 = K \frac{36}{16}\)


\(K = \frac{27 \times 16}{36}\)

\(K = 12\)

So the equation connecting P, Q and R is

\(P = \frac{12Q}{R}\)