9. A fort had enough food for 80 soldiers for 60 days. How long would the food last if 20 more soldiers join after 15 days? 10. 500 soldiers in a fort had enough food for 30 days. After 6 days, some soldiers were sent to another fort and thus the food lasted for 32 more days. How many soldiers left the fort?
Answer (1)
Problem 9:Given:Initial number of soldiers = 80Food lasts = 60 daysFood consumed by 80 soldiers for 60 days = 80 soldiers * 60 days = 4800 soldier-days of food.After 15 days, food consumed = 80 soldiers * 15 days = 1200 soldier-days.Remaining food:Total food = 4800 soldier-daysRemaining food after 15 days = 4800 - 1200 = 3600 soldier-days.Now, with 20 more soldiers:New number of soldiers = 80 + 20 = 100 soldiers.Finding how long the remaining food will last:Remaining food = 3600 soldier-daysIf there are 100 soldiers, the food will last for 3600 soldier-days100 soldiers=36 days100 soldiers3600 soldier-days =36 days.Answer: The food will last for 36 days after 15 days with the additional soldiers.
