The number of telephone calls N between two cities A and B varies directly as the population \(P_A\), P\(_B\) respectively and inversely as the square of the distance D between A and B. Which of the following equations represents this relation?
A
N = \(\frac{kp_A}{D^2} + {cp_B}{D^2}\)
B
N = \(\frac{k P_{A} P_{B} }{D^2}\)
C
N = \(\frac{kD_AP_D}{B^2}\)
D
N = \(\frac{kD^2_AP_D}{B}\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
\(N \propto P_{A}\); \(N \propto P_{B}\); \(N \propto \frac{1}{D^{2}}\)
\(\therefore N \propto \frac{P_{A} P_{B}}{D^{2}}\)
\(N = \frac{k P_{A} P_{B}}{D^{2}}\)
Source: Myschool Past Questions Archive (Record #32690)