1200 soldiers in a fort had enough food for 28 days.After 4 days ,some soldiers were transferred to another fort and thus , the food was enough for 32 more days.How many soldiers were transferred?



P.S.Want 1 answer done by proportional method and the other in unitary method.

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2015-04-23T20:13:22+05:30

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Total amount of food available initially:  1200 * 28    Soldier-days
After 4 days, the amount of food remaining:  1, 200 * 24  soldier-days worth.

Let N soldiers be remaining after some are transferred to another fort.

     1, 200 * 24  = N * 32
               N = 900
  Hence,  300 soldiers were transferred.

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Proportional method

     As the number of soldiers decreases, the number of days the food lasts will increases.  As the number of soldiers increases, the number of days the food lasts, will decrease.  So number N  of soldiers is inversely proportional to the number D of days.

               So    N = K / D,    where  K = constant of proportionality
                     when  N = 1,200  then  D = 24

             So  K = N D = 1,200 * 24
  
       When D = 32,  N = K / D = 1, 200 * 24 / 32 = 900

     Hence, there were only 900 soldier after 4 days.    So 1200 - 900 = 300 soldiers are transferred.

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Did you get D by doing 28-4?What will be the statement there?
N and D are inversely proportional to each other... Hence N2 / N1 = D2 / D1 or, N2 : N1 = D2 : D1
Or, you say, N and D are inversely proportional, So 24 : 1200 = 1 / (32 : N) OR, 24 : 1200 = N : 32
Sorry, my statement above was wrong... it should be : N and D are inversely proportional to each other... Hence N2 / N1 = D1 / D2 or, N2 : N1 = D1 : D2.
Now calculate N2 = N1 D1 / D2 or the other formula: N = 24 /1200 * 32 = 900