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Question
In a fort 150 men had provisions for 45 days. After 10 days, 25 men left the fort. How long would the food last at the same rate?
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Solution 1
After 10 days:
For 150 men, provision will last (45 − 10)
days = 35 days
⇒ For 1 man, the provisions will last
= 150 × 35 days
And for (150 − 25) = 125 men, the provisions
will last for =`(150xx35)/125`
= 42 days
Solution 2
Given:
- 150 men have food for 45 days.
- After 10 days, 25 men leave the fort.
- We need to find how long the remaining food will last for 125 men.
The total amount of food is:
Total food = 150⋅45 = 6750 man-days.
Food consumed by 150 men in 10 days is
Food consumed = 150⋅10 = 1500 man-days.
The remaining food after 10 days is
Remaining food = 6750 − 1500 = 5250 man-days.
After 25 men leave, the remaining men are:
Remaining men = 150 − 25 = 125.
The number of days the remaining food will last for 125 men is:
Remaining days = `"Remaining food"/"Remaining men"=5250/125`
= 42 days
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