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 1

The number of hours required to build a wall is inversely proportional to the number of workers employed.

Let the number of hours be h and the number of workers be w.

Here, h varies inversely as w i.e. $h\propto \frac{1}{w}$.

∴ $h=\frac{k}{w}$, where is k is constant of variation

⇒ h × w = k

When h = 48, w = 15.

∴ k = 48 × 15 = 720

So, the equation of variation is hw = 720.

When h = 30,

30w = 720

⇒ w = $\frac{720}{30}$ = 24

Thus, the number of workers required to do the same work in 30 hours is 24.