Question

A garrison of 1200 men has suffient rations for 25 days at the rate of 2400 g per day. If 300 men join them and the rations are reduced to 2000 g per man per day how long will the food last at all of them

Answer 1

The number of men increases by a ratio 1500/1200 = 5/4, so the food would last 4/5 as long if the same rations are maintained. However, since the rations are being reduced by a ratio 2000/2400 = 5/6 , the food will last 4/5 * 6/5 as long, or (24/25)*25, which is 24 days.