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# 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?

Video Solution
Direct And Inverse Proportions
Ex 13.2 | Question 5

## 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.

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