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

## 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.