Grass in lawn grows equally
thick and in a uniform rate. It takes 40 days for 40 cows and 60 days for 30
cows to eat the whole of the grass. How many days does it take for 20 cows to do
the same?

1) 80
2) 60
3) 120
4) 180

• let initial amount of grass = x units.
  let each cow eats 1 unit of grass everyday.
  so 40 cows eat 40 units of grass in 1 day
  and, 1600 (=40 x 40) units in 40 days.
  
  Since they have cleared the lawn, and grass increases at some rate, they must have eaten more than the initial amount of grass, i.e, x.
  
  Rate of growth of grass = (total grass eaten - initial amount) / number of days
  = (1600 - x) / 40 units per day.
  
  30 cows take 60 days to clear lawn, so equation becomes
  [x + {(1600 - x) /40} x 60] / 30 = 60
  
  => x = 1200 units.
  
  Rate of growth of grass = (1600 - 1200) / 40 = 10 units per day.
  
  Now, 20 cows eat 20 units per day and 10 units of grass grow everyday, so net consumption is 10 units.
  
  So, 1200 units of grass eaten at the rate of 10 units per day will take 120 days to finish :)
• 10 years agoHelpfull: Yes(1) No(1)