## January 5, 2009

### Lawn Puzzle

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?

ranjana said...

it will be 9

Secret SquÃ¯rrel said...

It depends on how the cows eat the grass.

If they simply eat the top of the grass, leaving the root systems intact, the grass will increase by the exact same absolute amount. (The question only says that the grass grows at the same rate and makes no mention of the amount - it's like the difference between simple and compound interest).

If the cows eat the grass in patches, removing the roots, and thus decreasing the grass's ability to grow back, it is more complicated to calculate.

Either way, 9 cows is way too low. More like 18.

a said...

i think its 20.let the rate of growth of grass be v...considering dat the rate of eating grass will be proportional to the no of cows..the rate of depletion of grass will be m*n,where n is no of cows and m is a constant...now..

m*n-v=r....r=net rate of depletion,
for the first case,
total grass depletes in 24 days with 70 cows...r=-k/24,k=total grass
hence eqn.....

m*70-v=-k/24

m*30-v=k/60

m*x-v=k/96
solving gives..
x=20...

hence the ans must be 20 cows..

EMPORiO said...