6 goats or 8 sheeps can graze a field in 50 days. 8 goats and 6 sheeps can graze the field in:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 24 days
Grazing the field is a fixed amount of work. An animal that would graze it alone in \(n\) days grazes \(\frac{1}{n}\) of it in a day, and the daily shares of animals grazing together are added.
One goat (6 goats take 50 days):
One goat alone would take \(6\times50=300\) days
It grazes \(\frac{1}{300}\) of the field a day
One sheep (8 sheep take 50 days):
One sheep alone would take \(8\times50=400\) days
It grazes \(\frac{1}{400}\) a day
8 goats and 6 sheep together (their daily shares are added):
In a day: \(\displaystyle\frac{8}{300}+\frac{6}{400}=\frac{32}{1200}+\frac{18}{1200}=\frac{50}{1200}=\frac{1}{24}\)
So they graze the whole field in 24 days