A playground can be grazed by 5 sheep in 5 days and 7 sheep in 3 days. how much time should be taken by 6 sheep to graze the playground completely??( grass grows on the playground at a complete rate) ans: 3.75 days

Let the initial grass be 'x' and the rate of growth be 'y'
So, grass grazed by 5 sheep in 5 days = x + 4y
Let each sheep graze 'k' amount of grass per day.
So, 5k*5 = 25k = x + 4y => k = (x + 4y)/25
Grass grazed by 7 sheep in 3 days = 7k * 3 = 21k = x + 2y => k = (x + 2y)/21
=> (x + 4y)/25 = (x + 2y)/21
=> 21x + 84y = 25x + 50y
=> 4x = 34y => x = 8.5y

Let 6 sheep take 'n' days to graze
=> x + (n-1)y = 6k * n
=> 8.5y + ny - y = n*6*(10.5y)/21
=> 7.5y + ny = 3ny
=> 2ny = 7.5y => n = 3.75