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?

Saturday, July 09, 2011

Question:

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?

Answer

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 are needed to eat the grass in 96 days.