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.