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

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.

∴ `n ∝ 1/t`

∴ n = `"k" = 1/t`

where k is the constant of variation

∴ n × t = k   …(i)

15 workers can build a wall in 48 hours,

i.e., when n = 15, t = 48

∴ Substituting n = 15 and t = 48 in (i), we get

n × t = k

15 × 48 = k

∴ k = 720

Substituting k = 720 in (i), we get

n × t = k

∴ n × t = 720    …(ii)
This is the equation of variation.

Now, we have to find the number of workers required to do the same work in 30 hours.
i.e., when t = 30, n = ?

∴ Substituting t = 30 in (ii), we get

n × t = 720

∴ n × 30 = 720

∴ n = `720/30`

∴ n = 24
∴ 24 workers will be required to build the wall in 30 hours.