text: A military garrison in a wild frontier has 600 men : GMAT Problem Solving (PS)
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  # A military garrison in a wild frontier has 600 men
  
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  A military garrison in a wild frontier has 600 men [#permalink]
  
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  21 Feb 2013, 21:05
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  A military garrison in a wild frontier has 600 men who have provisions to last 26 weeks. At the end of 6 weeks they are joined by another 300 men. How long will the provisions last?
  
  A. 13 1/3
  B. 12 1/3
  C. 11 3/3
  D. 12 1/2
  E. 12 3/4
  [Reveal] Spoiler: OA
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  Re: A military garrison in a wild frontier has 600 men [#permalink]
  
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  21 Feb 2013, 21:41
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  KUDOS
  Total provisions=600*26*7=109200
  
  Provisions used for in 6 weeks=6*7*600=25200
  
  remaining provisions=84000
  
  remaining provisions need to be split between 900(600+300) people.
  
  Number of provisions per person= 84000/900
  
  we need to find the answer in terms of weeks=(84000/900)/7=131/3
  
  Hope it helps!
  
  antoxavier wrote:
  A military garrison in a wild frontier has 600 men who have provisions to last 26 weeks. At the end of 6 weeks they are joined by another 300 men. How long will the provisions last?
  
  A. 13 1/3
  B. 12 1/3
  C. 11 3/3
  D. 12 1/2
  E. 12 3/4
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  Re: A military garrison in a wild frontier has 600 men [#permalink]
  
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  21 Feb 2013, 21:50
  antoxavier wrote:
  A military garrison in a wild frontier has 600 men who have provisions to last 26 weeks. At the end of 6 weeks they are joined by another 300 men. How long will the provisions last?
  
  A. 13 1/3
  B. 12 1/3
  C. 11 3/3
  D. 12 1/2
  E. 12 3/4
  
  Assume 1 group = 300 men, And 1 group can eat one box
  
  So.,
  52 boxes will cover 2 groups for 26 weeks
  
  In 6 weeks, 2 groups will have consumed 12 boxes.
  
  Remaining = 40 boxes
  New No. of groups = 3
  
  No. of weeks = 40/3 = 13.33
  
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  Re: A military garrison in a wild frontier has 600 men [#permalink]
  
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  22 Feb 2013, 00:51
  1
  KUDOS
  So we know that the number of the weeks of provision left is inversely proportional to the number of people.
  
  Thus, at the end of 6 weeks, the total provision left is for 20 weeks.
  
  Thus, $$600*20 = 900*x$$
  
  or $$x = \frac{40}{3} = 13.3333$$
  
  A.
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  Re: A military garrison in a wild frontier has 600 men [#permalink]
  
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  27 Jul 2014, 09:45
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  Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
  
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  Re: A military garrison in a wild frontier has 600 men   [#permalink] 27 Jul 2014, 09:45
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