1.

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.

∴ n ∝ 1/t

∴ n = k x (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 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.


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