Answer: C. For two equal waves forming a standing wave with a node at $x=0$ the amplitude at position $x$ is $2a|\sin(2\pi x/\lambda)|$ Thus $A_P=a$ and $A_Q=\sqrt{3}a$ giving $A_P/A_Q=1/\sqrt{3}$ Both points lie between the same pair of adjacent nodes, so their oscillations are in phase and their phase difference is $0$

A: reverses the requested amplitude ratio.
B: finds the ratio correctly but treats points in the same segment between nodes as oscillating in antiphase.
D: assumes amplitude is proportional to distance from the node, giving $x_P/x_Q=1/4$

Remember: points in the same segment between adjacent nodes oscillate in phase.