Question

Alex has 3 horses a, b and c at his farm house. The horses graze the grass from the field at alex's farmhouse. 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 graze 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

Answer 1

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 can graze on the field together for a period of 40 days.

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