Math, asked by ABAbhishek7191, 1 year ago

3 horses A, B and C at his farm house. The horses graze the grass from the field at Alex’s farm house. Alex notices that: * When horses A & B graze the field together, they graze all the grass after 45 days. * When the horses A and C graze on the field together, there is no more grass after 60 days. * When the horse A grazes on the field alone, there is no more grass after 90 days. * When the horses B and C graze on the field together, there is no more grass after 90 days also. For how long can the three horses graze on the field together?

Answers

Answered by bhagyashreechowdhury
0

The three horses A, B & C can graze on the field together for 40 days.

Step-by-step explanation:

It is given,

Horse “A & B” together can graze the complete grass on field in 45 days

Horse “A & C” together can graze the complete grass on field in 60 days

Horse “A” alone can graze the complete grass on field in 90 days

Horse “B & C” together graze the complete grass on field in 90 days

So, we get

Horse (A+B)’s 1-day grazing = \frac{1}{45}

Horse (B+C)’s 1-day grazing = \frac{1}{90}

Horse (C+A)’s 1-day grazing = \frac{1}{60}

Now,  

(A+B+C)’s together 1-day grazing will take,

= ½ * [\frac{1}{45} + \frac{1}{90} + \frac{1}{60} ]

= ½ * \frac{4+3+2}{180}

= ½ * \frac{9}{180}

= ½ * \frac{1}{20}

= \frac{1}{40}

Thus, the three horses A, B & C can graze on the field together for a period of 40 days.

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