The relationship between Frugal and Extravagant is that they are antonyms. Frugal means sparing or economical with regard to money or food. Extravagant means lacking restraint in spending money or using resources. They are opposites.
Let's analyze the options to find another pair of antonyms:
\[\begin{array}{rl} \bullet & \text{(A) Predecessor : Precursor: These are synonyms (something that comes before).} \\ \bullet & \text{(B) Hermit : Philosopher: These are different roles, not opposites.} \\ \bullet & \text{(C) Teacher : Philanthropist: These are different roles, not opposites.} \\ \bullet & \text{(D) Criticise : Advocate: To criticise means to point out the faults of. To advocate means to publicly recommend or support. These actions are opposite in nature.} \\ \end{array}\]
The pair that best represents an antonym relationship is Criticise : Advocate.