Grass in lawn grows equally thick and in a uniform rate. It takes 24 days for 70 cows and 60 days for 30 cows to eat the whole of the grass. How many cows are needed to eat the grass in 96 days.?

• I think this approach is very long to solve this problem i try to reduce some step
  g= grass initially, r= rate at which grass grow/day, c= cow eat grass/day
  g+24r=70*24c=1680c-----------1
  g+60r=60*30c=1800c--------->g=1800c-60r----------------2
  by solving this 2 equation we have relation c=(3/10)r-------------3
  g+96r=96nc
  =>96nc=1800c-60r+96r=1800c+36r=1800c+120c=1920c
  =>n=20
  Please if someone find shorter approach to solver this problem then post here
• 12 years agoHelpfull: Yes(10) No(3)
• 20 cows
  
  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
  
  Hence, 20 cows a
• 13 years agoHelpfull: Yes(7) No(0)
• 20 days to take grass in 96 day. .
• 9 years agoHelpfull: Yes(2) No(2)
• use ratio and proportion
• 8 years agoHelpfull: Yes(2) No(0)
• 20 cows
• 14 years agoHelpfull: Yes(1) No(3)