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# Proportions Watch

1. A fort had provisions for 300 men for 90 days. After 20 days, 50 men left the fort. How long would the food last at the same rate.

So men is inversely proportional to days

so with 300 and 90 the constant is 27000

if you use the fact that after 20 days 50 men left you can use 250 men and you get 108 days is that correct?
2. (Original post by uzer)
A fort had provisions for 300 men for 90 days. After 20 days, 50 men left the fort. How long would the food last at the same rate.

So men is inversely proportional to days

so with 300 and 90 the constant is 27000

if you use the fact that after 20 days 50 men left you can use 250 men and you get 108 days is that correct?
I'm not clear what the question is asking.

If it means how long would the food last if there had been 250 men there all the time, then yes, 108.

Alternatively, it could mean how long does the food now last, given 300 men used it for 20 days, and now 250 men are using what's left; which would give a different result.
3. (Original post by Natalo77)
Any questions, send me a message or tag me
Please don't post full solutions straight off (see guidelines at top of forum), particularly as it's incorrect.
4. I think 300 men ate for 20 days and then 50 left and 250 ate the remainder of the food. So I think in that case the answer would be 84 days is that correct?

Not a very well worded question
5. (Original post by uzer)
I think 300 men ate for 20 days and then 50 left and 250 ate the remainder of the food. So I think in that case the answer would be 84 days is that correct?

Not a very well worded question
Agreed. Though I would say a "further 84 days", to make it clear that it's on top of the initial 20.

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