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 his cattle?

Answer 1

Let the number of days be $x$

Total number of animals$=20+10=30$

Animals	$20$	$30$
Number of Days	$6$	$x$

The number of days and animals are inversely proportional

Therefore, from inverse proportionality property, we have,

$$\begin{gathered} 20\times 6=30\times x \\ \Rightarrow 120=30x \\ \Rightarrow x=\frac{120}{30} \\ \Rightarrow x=4 \end{gathered}$$

Hence, if there were $30$ animals, the food will last for $4$ days.