Give,
Total Soldiers = 200
Food for them = 31 days
So, Quantity of food = 200 *31 = 6200 man-days
Till 27 days, quantity consumed = 27 *200 = 5400 man-days
Rest quantity = 6200 - 5400 = 800 man-days
Remaining soldiers = 200 - 120 = 80
Let remaining food will sufficient for x days
Now,
5400 + 80 x = 6200
80 x = 800
x = 10 days