Quantity of food = 200 X 31 = 6200 man-days
Till 27 days, quantity consumed = 27 X 200 = 5400 man-days
Remaining quantity = 6200 –5400 = 800 man days
Remaining soilders = 200 –120 = 80
Let remaining food will be sufficient for x days⇒5400 + 80x = 6200⇒x= 10 days