If 15 workers can build a wall in 48 hours, how many workers will…

Question

If 15 workers can build a wall in 48 hours, how many workers will be required to do the same work in 30 hours ?

✓

Answer

Let, $n$ represent the number of workers building the wall and t represent the time required.
Since, the number of workers varies inversely with the time required to build the wall.
$
\begin{aligned}
& \therefore n \propto \frac{1}{\mathrm{t}} \\
& \therefore n=\mathrm{k} \times \frac{1}{\mathrm{t}}
\end{aligned}
$
where $\mathrm{k}$ is the constant of variation
$
\therefore \mathrm{n} \times \mathrm{t}=\mathrm{k........(i)}
$
15 workers can build a wall in 48 hours,
i.e., when $n=15, t=48$
$\therefore$ Substituting $n=15$ and $t=48$ in (i), we get
$
\begin{aligned}
& \mathrm{n} \times \mathrm{t}=\mathrm{k} \\
& \therefore 15 \times 48=\mathrm{k} \\
& \therefore \mathrm{k}=720
\end{aligned}
$
Substituting $k=720$ in (i), we get
$
\begin{aligned}
& n \times t=k \\
& \therefore n \times t=720 \text {...(ii) }
\end{aligned}
$
This is the equation of variation.
Now, we have to find number of workers required to do the same work in 30 hours.
i.e., when $t=30, \mathrm{n}=$ ?
$\therefore$ Substituting $\mathrm{t}=30$ in (ii), we get
$\mathrm{n} \times \mathrm{t}=720$
$\therefore \mathrm{n} \times 30=720$
$\therefore n=\frac{720}{30}$
$\therefore \mathrm{n}=24$
$\therefore 24$ workers will be required to build the wall in 30 hours.