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