# Ex.13.2 Q8 Direct and Inverse Proportions Solution - NCERT Maths Class 8

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## Question

A factory requires $$42$$ machines to produce a given number of articles in $$63$$ days. How many machines would be required to produce the same number of articles in $$54$$ days?

## 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.

${x_1}{y_1} = {x_2}{y_2}$

What is Known:

$$42$$ machines to produce a given number of articles in $$63$$ days.

What is Unknown:

Machines required for producing same no. of articles in $$54$$ days.

Steps:

If the number of days decreases the machine required will increase. So, it is an inverse proportion.

\begin{align}{{\rm{x}}_1}{{\rm{y}}_1} &= {{\rm{x}}_2}{{\rm{y}}_2}\\42 \times 63 &= 54 \times {{\rm{y}}_2}\\{y_2} &= \frac{{42 \times 63}}{{54}}\\{{\rm{y}}_2} &= 49\end{align}

$$49$$ machines will be required to produce the same number of articles in $$54$$ days.

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