Question

7. The amount of sheep In a field is Inversely proportional to the time taken for them to
eat all of the grass in the field. When there are 100 sheep in a field it takes them 28
days to eat all of the grass. How many days would it take 45 sheep to eat all of the
grass?​

Answer 1

A n s w e r

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G i v e n

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• 100 sheep in a field takes 28 days to eat all of the grass

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F i n d

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• Days would it take 45 sheep to eat all of the grass

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S o l u t i o n

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Given that the sheep In a field is Inversely proportional to the time taken for them to eat all of the grass in the field , thus if the sheeps increases the days required to eat grass would decreases and vice versa

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We would be calculating the total grass that need to be eaten

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With 100 sheeps

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$\underline{ \underline{\bold{\texttt{Total grass :}}}}$

$\:\:$

: ➜ Total grass = Sheep × Days

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• Sheep = 100

• Days = 28

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⟮ Putting the above values ⟯

$\:\:$

: ➜ Total grass = Sheep × Days

$\:\:$

: ➜ Total grass = 100 × 28

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: ➜ Total grass = 2800 units

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• Hence the total grass is 2800 units

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With 45 sheeps

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Clearly the total grass would remain same thus ,

$\:\:$

$\underline{ \underline{\bold{\texttt{Total grass :}}}}$

$\:\:$

: ➜ Total grass = Sheep × Days

$\:\:$

• Total grass = 2800

• Sheep = 45

• Days = x

$\:\:$

⟮ Putting the above values ⟯

$\:\:$

: ➜ Total grass = Sheep × Days

$\:\:$

: ➜ 2800 = 45 × x

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: ➜ $\sf x = \dfrac { 2800 } { 45 }$

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: : ➨ x ≈ 62 days

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• Hence 45 sheeps will take approximately 62 days

Answer 2

A n s w e r

$\:\:$

G i v e n

$\:\:$

• 100 sheep in a field takes 28 days to eat all of the grass

$\:\:$

F i n d =?

$\:\:$

• Days would it take 45 sheep to eat all of the grass

$\:\:$

S o l u t i o n

$\:\:$

• Given that the sheep In a field is Inversely proportional to the time taken for them to eat all of the grass in the field , thus if the sheeps increases the days required to eat grass would decreases and vice versa

$\:\:$

We would be calculating the total grass that need to be eaten

$\:\:$

With 100 sheeps

$\:\:$

$\underline{ \underline{\bold{\texttt{Total grass :}}}}$

$\:\:$

: ➜ Total grass = Sheep × Days

$\:\:$

Sheep = 100

Days = 28

$\:\:$

⟮ Putting the above values ⟯

$\:\:$

: ➜ Total grass = Sheep × Days

$\:\:$

: ➜ Total grass = 100 × 28

$\:\:$

: ➜ Total grass = 2800 units

$\:\:$

Hence the total grass is 2800 units

$\:\:$

With 45 sheeps

$\:\:$

Clearly the total grass would remain same thus ,

$\:\:$

$\underline{ \underline{\bold{\texttt{Total grass :}}}}$

$\:\:$

: ➜ Total grass = Sheep × Days

$\:\:$

Total grass = 2800

Sheep = 45

Days = x

$\:\:$

⟮ Putting the above values ⟯

$\:\:$

: ➜ Total grass = Sheep × Days

$\:\:$

: ➜ 2800 = 45 × x

$\:\:$

: ➜ $\sf x = \dfrac { 2800 } { 45 }$

$\:\:$

: : ➨ x ≈ 62 days

$\:\:$

Hence 45 sheeps will take approximately 62 days