Question

A farmer has enough food to feed 28 animals in his cattle for 9 days. How long would the food last, if there were 8 more animals in his cattle?

Answer 1

Let x be the required number of days. Then, we have:

No. of days	9	x
No. of animals	28	36

Clearly, more number of animals will take less number of days to finish the food.
So, it is a case of inverse proportion.
$$\begin{gathered} \mathrm{Now},9\times 28=x\times 36 \\ \Rightarrow x=\frac{9\times 28}{36} \\ \Rightarrow x=7 \end{gathered}$$

Therefore, the food will last for 7 days.