Ex.13.2 Q5 Direct and Inverse Proportions Solution - NCERT Maths Class 8

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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?

Text Solution

Reasoning:

Two numbers \(x\) and \(y\) are said to vary in inverse proportion if

\[\begin{align}xy = {\rm{ }}k,{\rm{ }}x{\rm{ }} = {\rm{ }}\frac{1}{y}k\end{align}\]

Where \(k\) is a constant.

\[\begin{align}{x_1}{y_1} = {x_2}{y_2}\end{align}\]

What is Known:

In a cattle, food is for \(20\) animals for \(6\) days.

What is Unknown:

The number of days for \(30\) animals \((20 + 10 = 30)\)

Steps:

If the number of animals increases the number of days they can be fed will decrease, so it is in the inverse proportion.

\[\begin{align}{x_1}{y_1}& = {x_2}{y_2}\\20 \times 6 &= 30 \times {y_2}\\{y_2} &= \frac{{20 \times 6}}{{30}}\\{y_2} &= 4\end{align}\]

The food would last for \(4\) days for \(30\) animals.