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?

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Solution

## 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 proportionalTherefore, from inverse proportionality property, we have,$20×6=30×x\phantom{\rule{0ex}{0ex}}⇒120=30x\phantom{\rule{0ex}{0ex}}⇒x=\frac{120}{30}\phantom{\rule{0ex}{0ex}}⇒x=4$Hence, if there were $30$ animals, the food will last for $4$ days.

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