Question

A farmer has enough food to feed 20 animals in his cattle for 6 days. How long would the food last, if there were 10 more animals in the cattle?

Answer 1

Hint: In this question, first write down the given details, here the food required to feed Number of animals is inversely proportional to number of days food is available.

Complete step-by-step answer:
Given that the farmer has enough food to feed 20 animals in his cattle for 6 days.
Let the number of days food can be fed be X.
Now the farmer is having enough food to feed 20 animals for a period of 6 days. Later the farmer added 10 more animals to the cattle.
Now, the total number of animals in the cattle are 30. Therefore, we should find out for how many days the food is available for 30 animals.
\[ \Rightarrow \dfrac{{20}}{{(20 + 10)}} = \dfrac{X}{6}\]
\[ \Rightarrow \dfrac{{20}}{{30}} = \dfrac{X}{6}\]
\[ \Rightarrow \dfrac{2}{3} = \dfrac{X}{6}\]
\[\therefore X = \dfrac{2}{3} \times 6 = 4\]
Now, the number of days required to feed 30 animals is: \[X = 4\]
Therefore, for 4 days a farmer can feed 30 animals in his cattle.

Note: The number of days food is available is inversely proportional to number of animals. Since there is an increase in the number of animals, the days for which the food is enough will be reduced. That’s why the number of days food is available is inversely proportional to the number of animals. If the number of days we obtained is more than 6 for 30 animals then our answer is incorrect. It should be less than 6 days. In this way we can check our answer.