Question 337451
The answer should be 300 days.
1 sheep eat 1 unit of grass per day.
200 sheep will eat 200 units of grass per day.
200 sheep will eat 200 x 100 = 20000 units of grass in 100 days.
150 sheep will eat 150x150 = 22500 units of grass in 150 days.
Hence in 50 days the grass grew 22500 - 20000 = 2500 units
in 1 day the grass will grow 2500/50 = 50 units
In 100 days, the grass would have grown 50 x 100 = 5000 units.
hence initial grass = 20000 - 5000 = 15000 units
Days taken for 100 sheep to eat up the grass = X.
15000 + 50X = 100X
50X = 15000
X = 300 days.