Question

If 15 workers can finish a task in 42 hours, calculate the number of workers required to complete the same task in 30 hours.

Answer 1

In this situation, the number of workers varies indirectly with the time required to finish a task.

Thus, they are inversely proportional.

Now, assume that the number of workers required to complete the task in 30 hours be “x”.

Here, the number of workers ∝ 1/hours

Or,

Number of workers = C/hours (here “C” is the constant of proportionality)

Now, consider the first case: “15 workers can finish a task in 42 hours”

Here, 15 = C/42

=> C = 15 × 42 = 630.

Now, consider the second case: “x workers can finish a task in 30 hours”

Here, x = C/30

=> x = 630/30

Or, x = 21

So, the number of 21 workers are required to complete the task in 30 hours.

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Answer 2

In this situation, the number of workers varies indirectly with the time required to finish a task.

Thus, they are inversely proportional.

Now, assume that the number of workers required to complete the task in 30 hours be “x”.

Here, the number of workers ∝ 1/hours

Or,

Number of workers = C/hours (here “C” is the constant of proportionality)

Now, consider the first case: “15 workers can finish a task in 42 hours”

Here, 15 = C/42

=> C = 15 × 42 = 630.

Now, consider the second case: “x workers can finish a task in 30 hours”

Here, x = C/30

=> x = 630/30

Or, x = 21

So, the number of 21 workers are required to complete the task in 30 hours.