In a Grass field if 40 cows could eat for 40 days.the same grass field could eat 30 cows for 60 days.how long will it feed 20 cows?

• 80 days.
  
  If 10 Cows are decreased, 20 days are increased.
  
  So 30 cows could eat for 60 days and 20 cows could eat for 80 days.
• 12 years agoHelpfull: Yes(16) No(3)
• 120 days.
  
  If P is present grass amount
  g is growth of grass per day
  C is grass consumed by one cow per day
  then
  P+40g = 1600*C
  P+60 g = 1800*C
  
  solving these eqns, we get
  g = 10C
  and
  P= 1200*C
  
  Hence
  If d is no. of days taken by 20 cows, then
  1200*C + d*10*C = 20*d*C
  hence d= 120 days
• 12 years agoHelpfull: Yes(10) No(4)
• Here is how I solved the problem. First we need to split the problem down into two parts. The growth of grass and how many cows it can feed, and the excess grass in the field at the start and how many cows that can feed.
  
  40 cows feeding for 40 days = 1600 cowdaysfood (40*40)
  30 cows feeding for 60 days = 1800 cowdaysfood (30*60)
  
  In those extra 20 days, the cows have eaten an extra 200 cowdaysfood which must have grown in those 20 days. Therefore:
  
  20 days growth of grass produces 200 cowdaysfood
  40 days growth of grass produces 400 cowdaysfood
  1 days growth of grass produces 10 cowdaysfood
  
  Therefore the growth of grass can sustain 10 cows indefinitely, or at least until the grass stops growing. We now need to work out how much excess grass was in the field and how long it will last.
  
  If 1600 cowdaysfood were consumed in 40 days
  and 400 cowdaysfood grew in 40 days
  then 1200 cowdays food must have been the excess (1600-400)
  
  The qustion asked about a field of 20 cows. 10 of them could feed for ever on the new growth. The other 10 must feed on the excess. That will last them 120 days (1200/10). So the answer is 120 days.
  
  Or to put it more mathematically:
  
  x = 1200 / (y - 10)
  
  where x = the number of days and y = the number of cows
• 12 years agoHelpfull: Yes(8) No(0)
• I think Grass is growing during this period. That is why there is confusion.
• 12 years agoHelpfull: Yes(5) No(7)
• PARGAT PAL SINGH IS CHUTIA
• 8 years agoHelpfull: Yes(3) No(3)
• i think this puzzle is not clear because according to first condition 20 cows can eat for 80 days ...............
  while from other condition 20 cows can feed for 90 days..........
  rule.................
  one cow can feed 40*40 days
  so for 20.................{40*40}/20=80
  as same.............................................
• 12 years agoHelpfull: Yes(2) No(2)
• 40 cows take 40 Days.
  and 30 cows take 60 Days.
  Its obvious that 10 cows less 20 days More.
  So, 20 Cows will take 80 Days.
• 5 years agoHelpfull: Yes(0) No(0)