# 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.

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