Grass In Lawn Grows Equally Thick And In A Uniform Rate. It Takes 40

1.	Grass In Lawn Grows Equally Thick And In A Uniform Rate. It Takes 40 Days For 40 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» Let quantity of grass initially = g Let r be the rate at which grass grow in 1 day, Let c be the quantity of grass a cow EAT in 1 day we can deduce from ‘. It takes 40 days for 40 COWS and 60 days for 30 cows to eat the whole of the grass’ that ⇒ g + 40r = 40 × 40c = 1600c-----------[1] and ⇒ g + 60r = 60 × 30c = 1800c ⇒ g = 1800c - 60r----------------2 Putting this value of g in eqn [1] we have ⇒ 1800c – 60r + 40r = 1600c ⇒ 200c = 20r ⇒ C = 0.1 r ⇒ r = 10c Let m be the number of days required by 20 cows to eat the entire of the field = m Then We have the eqn as ⇒ g + 96r = 96nc ⇒ 96nc = 1800c - 60r + 96r (as we have g=1800c-60r from eqn 2) ⇒ 96nc = 1800c + 36r ⇒ 96nc = 1800c+ 36 × 10c ⇒ 96nc = 1800c + 360c ⇒ 96nc = 2160c HENCE we have 96nc = 2160c Dividing both the sides by 96C We get ⇒ N = 22.5 Let quantity of grass initially = g Let r be the rate at which grass grow in 1 day, Let c be the quantity of grass a cow eat in 1 day we can deduce from ‘. It takes 40 days for 40 cows and 60 days for 30 cows to eat the whole of the grass’ that ⇒ g + 40r = 40 × 40c = 1600c-----------[1] and ⇒ g + 60r = 60 × 30c = 1800c ⇒ g = 1800c - 60r----------------2 Putting this value of g in eqn [1] we have ⇒ 1800c – 60r + 40r = 1600c ⇒ 200c = 20r ⇒ C = 0.1 r ⇒ r = 10c Let m be the number of days required by 20 cows to eat the entire of the field = m Then We have the eqn as ⇒ g + 96r = 96nc ⇒ 96nc = 1800c - 60r + 96r (as we have g=1800c-60r from eqn 2) ⇒ 96nc = 1800c + 36r ⇒ 96nc = 1800c+ 36 × 10c ⇒ 96nc = 1800c + 360c ⇒ 96nc = 2160c Hence we have 96nc = 2160c Dividing both the sides by 96c We get ⇒ n = 22.5

Grass In Lawn Grows Equally Thick And In A Uniform Rate. It Takes 40 Days For 40 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»

Let quantity of grass initially = g

Let r be the rate at which grass grow in 1 day,

Let c be the quantity of grass a cow EAT in 1 day

we can deduce from ‘. It takes 40 days for 40 COWS and 60 days for 30 cows to eat the whole of the grass’ that

⇒ g + 40r = 40 × 40c = 1600c-----------[1]

and

⇒ g + 60r = 60 × 30c = 1800c

⇒ g = 1800c - 60r----------------2

Putting this value of g in eqn [1]

we have

⇒ 1800c – 60r + 40r = 1600c

⇒ 200c = 20r

⇒ C = 0.1 r

⇒ r = 10c

Let m be the number of days required by 20 cows to eat the entire of the field = m

Then

We have the eqn as

⇒ g + 96r = 96nc

⇒ 96nc = 1800c - 60r + 96r (as we have g=1800c-60r from eqn 2)

⇒ 96nc = 1800c + 36r

⇒ 96nc = 1800c+ 36 × 10c

⇒ 96nc = 1800c + 360c

⇒ 96nc = 2160c

HENCE we have 96nc = 2160c

Dividing both the sides by 96C

We get

⇒ N = 22.5

Let quantity of grass initially = g

Let r be the rate at which grass grow in 1 day,

Let c be the quantity of grass a cow eat in 1 day

we can deduce from ‘. It takes 40 days for 40 cows and 60 days for 30 cows to eat the whole of the grass’ that