Ex.13.2 Q6 Direct and Inverse Proportions Solution - NCERT Maths Class 8

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Question

 A contractor estimates that \(3\) persons could rewire Jaswinder’s house in \(4\) days. If he uses \(4\) persons instead of \(3\), how long should they take to complete the job?

Text Solution

 

What is Known?

\(3 \) persons can rewire the house in \(4\) days.

What is Unknown?

Number of days when \(4\) persons do the job.

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.

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

Steps:

If the number of persons doing the job increases the day will increase so it is inverse proportion.

\[\begin{align}{x_1}{y_1} &= {x_2}{y_2}\\3 \times 4 &= 4{\rm{ }} \times {\rm{ }}{y_2}\\{y_2} &= \frac{{3\; \times \;4}}{4}\\{y_2} &= 3\end{align}\]

\(4\) persons will take \(3\) days to complete the job.