Concept: The question tests on the basics of Rates(Time and Work)
Solution:
Initial food = (190 * 4000) man days
After 30 days the remaining food is there for 160 * 4000 Man days
Since 800 troops leave, the food will last for a different number of days. Let this = x
Remaining Man days = (4000 - 800) * x = 3200x
Therefore 160 * 4000 = 3200x
x = 200 days
Option B