Concept:
Vitamin K is fat-soluble and requires bile for absorption. Bile duct obstruction can cause vitamin K deficiency, leading to prolonged PT due to reduced vitamin K-dependent clotting factors.
Step 1: Recall vitamin K-dependent factors.
Vitamin K is needed for synthesis of:
\[
II,\ VII,\ IX,\ X,\ Protein\ C,\ Protein\ S
\]
Step 2: Identify condition causing deficiency.
Bile duct obstruction reduces bile flow into the intestine. This impairs absorption of fat-soluble vitamins, including vitamin K.
Step 3: Choose condition where vitamin K helps.
Therefore, parenteral vitamin K will help in:
\[
\text{Bile duct obstruction}
\]