Mathematics
posted by Elizabeth on .
A garrison of 1200 men has sufficient ratios for 25 days at the rate of 2400g per man per day. If 300 man join them and the ratios are reduced to 2000g per man per day,how long will the road last all of them?
Thank you :)

1500 men at 2Kg/man day > 3000 Kg needed per day
1200 *2.4 Kg/man day *25 days = 72,000 Kg availablee
3000 * number of days = 72,000
so
days = 24 days 
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.