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500 soldiers in a fort had enough water for 10 days after 3 days some soldiers were transferred to another first and thus the water lasted for 20, more days how many soldiers were transferred
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500 soldiers in a fort had enough water for 10 days after 3 days some ...
Solution:
Let's analyze the given information step by step to find the number of soldiers transferred.
Step 1: Calculate the water consumption rate per soldier per day.
Given that 500 soldiers had enough water for 10 days, we can calculate the total water consumption as:
500 soldiers * 10 days = 5000 soldier-days
Hence, the water consumption rate per soldier per day is:
Total water consumption / Total number of soldiers = 5000 soldier-days / 500 soldiers = 10 soldier-days per soldier
Step 2: Calculate the total water available initially.
If the water lasted for 10 days with 500 soldiers, then the total water available initially can be calculated as:
Total water available = water consumption rate per soldier per day * total number of soldiers * number of days
= 10 soldier-days per soldier * 500 soldiers * 10 days = 5000 soldier-days
Step 3: Calculate the total water consumed in the first 3 days.
Since the water lasted for 10 days with 500 soldiers, the total water consumed in the first 3 days can be calculated as:
Total water consumed in the first 3 days = water consumption rate per soldier per day * total number of soldiers * number of days
= 10 soldier-days per soldier * 500 soldiers * 3 days = 1500 soldier-days
Step 4: Calculate the remaining water after the first 3 days.
The remaining water after the first 3 days can be calculated as:
Remaining water = Total water available - Total water consumed in the first 3 days
= 5000 soldier-days - 1500 soldier-days = 3500 soldier-days
Step 5: Calculate the new number of soldiers after the transfer.
Since the remaining water lasted for 20 more days, the new number of soldiers after the transfer can be calculated as:
New number of soldiers = Remaining water / (water consumption rate per soldier per day * number of days)
= 3500 soldier-days / (10 soldier-days per soldier * 20 days) = 17.5 soldiers
However, we cannot have a fraction of a soldier. So, it means that some soldiers must have been transferred to another fort.
Step 6: Calculate the number of soldiers transferred.
The number of soldiers transferred can be calculated as the difference between the total number of soldiers initially and the new number of soldiers after the transfer:
Number of soldiers transferred = Total number of soldiers initially - New number of soldiers after the transfer
= 500 soldiers - 17.5 soldiers = 482.5 soldiers
Again, we cannot have a fraction of a soldier. Therefore, we can conclude that approximately 483 soldiers were transferred to another fort.
Let's analyze the given information step by step to find the number of soldiers transferred.
Step 1: Calculate the water consumption rate per soldier per day.
Given that 500 soldiers had enough water for 10 days, we can calculate the total water consumption as:
500 soldiers * 10 days = 5000 soldier-days
Hence, the water consumption rate per soldier per day is:
Total water consumption / Total number of soldiers = 5000 soldier-days / 500 soldiers = 10 soldier-days per soldier
Step 2: Calculate the total water available initially.
If the water lasted for 10 days with 500 soldiers, then the total water available initially can be calculated as:
Total water available = water consumption rate per soldier per day * total number of soldiers * number of days
= 10 soldier-days per soldier * 500 soldiers * 10 days = 5000 soldier-days
Step 3: Calculate the total water consumed in the first 3 days.
Since the water lasted for 10 days with 500 soldiers, the total water consumed in the first 3 days can be calculated as:
Total water consumed in the first 3 days = water consumption rate per soldier per day * total number of soldiers * number of days
= 10 soldier-days per soldier * 500 soldiers * 3 days = 1500 soldier-days
Step 4: Calculate the remaining water after the first 3 days.
The remaining water after the first 3 days can be calculated as:
Remaining water = Total water available - Total water consumed in the first 3 days
= 5000 soldier-days - 1500 soldier-days = 3500 soldier-days
Step 5: Calculate the new number of soldiers after the transfer.
Since the remaining water lasted for 20 more days, the new number of soldiers after the transfer can be calculated as:
New number of soldiers = Remaining water / (water consumption rate per soldier per day * number of days)
= 3500 soldier-days / (10 soldier-days per soldier * 20 days) = 17.5 soldiers
However, we cannot have a fraction of a soldier. So, it means that some soldiers must have been transferred to another fort.
Step 6: Calculate the number of soldiers transferred.
The number of soldiers transferred can be calculated as the difference between the total number of soldiers initially and the new number of soldiers after the transfer:
Number of soldiers transferred = Total number of soldiers initially - New number of soldiers after the transfer
= 500 soldiers - 17.5 soldiers = 482.5 soldiers
Again, we cannot have a fraction of a soldier. Therefore, we can conclude that approximately 483 soldiers were transferred to another fort.
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