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?

 Video Solution
Direct And Inverse Proportions
Ex 13.2 | Question 8

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.

\[\begin{align} x_1 y_1 &= x_2 y_2 \\42 \times 63 &= 54 \times y_2 \\{y_2} &= \frac{{42 \times 63}}{{54}}\\y_2 &= 49\end{align}\]

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