A lawn has equally distributed grass. It takes 24 days to 70 cows and 60 days to 30 cows to eat the whole of grass. How many cows will be needed to eat the grass in 96 days.

• if a cow eats a certain amount of grass in the first day, then there should have grown a certain amount of grass on the next day...
  
  so if "g" is the initial amount of grass, then "x" amount of grass should have grown on the next day...
  so total grass for 2 days ==> g + x
  for 24 days, total grass ll be ==> g + 24x
  to eat the total grass of g+24x--> 70 cows are needed
  so g + 24x = 24 * 70 --> (1)
  similarly g + 60x = 60 * 30 -->(2)
  
  Solving (1) nd (2), v ll get
  g = 1600, x= 10/3
  
  now for 96 days, amount of grass grown daily ll be 96x
  so g + 96x = 96 * y [Let y be the no. of cows needed to eat g + 96x grass]
  1600 + 96*(10/3) = 96y
  y = 1920/96
  y = 20 cows are needed to eat the grass in 96 days
  
  Ans : 20 cows
• 10 years agoHelpfull: Yes(27) No(2)
• g - grass at the beginning
  
  r - rate at which grass grows, per day
  
  y - rate at which one cow eats grass, per day
  
  n - no of cows to eat the grass in 96 days
  
  g + 24*r = 70 * 24 * y
  
  g + 60*r = 30 * 60 * y
  
  g + 96*r = n * 96 * y
  
  Solving, n = 20.
• 10 years agoHelpfull: Yes(2) No(0)
• cows=(24*70+60*30)/96
• 10 years agoHelpfull: Yes(1) No(2)
• g - grass at the beginning
  r - rate at which grass grows, per day
  y - rate at which one cow eats grass, per day
  n - no of cows to eat the grass in 96 days
  
  From given data,
  g + 24*r = 70 * 24 * y ---------- A
  g + 60*r = 30 * 60 * y ---------- B
  g + 96*r = n * 96 * y ---------- C
  
  Solving for (B-A),
  (60 * r) - (24 * r)
  = (30 * 60 * y) - (70 * 24 * y) 36 * r
  = 120 * y ---------- D
  
  Solving for (C-B),
  (96 * r) - (60 * r)
  = (n * 96 * y) - (30 * 60 * y) 36 * r
  = (n * 96 - 30 * 60) * y 120 * y
  = (n * 96 - 30 * 60) * y
  
  [From D] 120 = (n * 96 - 1800)
  n = 20
  
  
• 7 years agoHelpfull: Yes(0) No(0)