Question

a garrison of 800 men had provisions for 39 days. however a reinforcement of 500 men arrived.for how many days will the food last now?

Answer 1

1200  men  has  food  provisions  for  25  days.
So,  number  of  men  [ x ]  =  1200  ,  300
  number  of  days  [ y ]  =  25  ,  y2
When  there  are  more  men,  food  provisions  for  them  will  be  there  for  less  days.
When  there  are  less  men,  food  provisions  for  them  will  be  there  for  more  days.
So,  it  is  an  inverse  proportion.
So,  x1y1  =  x2y2
ie,  1200  *  25  =  300  *  y2
So,  y2  =  1200  *  25  /  300
=  30000  /  300
=  100
So,  if  there  are  300  men,  the  food  will  last  for  100  days.

Comments

hi.
the question says reinforcements of 500 men which means that in total there will be 1300 men and not 300.
Also for 300 men, food provisions would be 104 days.

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Thats the point

Answer 2

800 men have food provision for 39 days

which implies that 100 men have food provision for 39*8=312 days

hence, 800+500=1300 men have food provisions for 312/13=24 days.