Right answer is (c) \(\frac{[A_{org}]}{[A_w]}\)
To explain: The above reaction represents a biphasic system consisting of a mixture of an aqueous and an organic solvent. Kw and Korg represents equilibrium constants for water and organic phase respectively. PA and PB are partition co-efficients of A and B respectively.
Korg = \(\frac{[B_{org}]}{[A_{org}]}\)
PB = \(\frac{[B_{org}]}{[B_w]}\)
Kw = \(\frac{[B_w]}{[A_w]}\)
Partition coefficient for A is represented by PA = \(\frac{[A_{org}]}{[A_w]}\),
Where Aorg and Aw are the concentration of A in organic solvent and water respectively.