If a task can be completed by 45 people in 20 days, then 75 people will take ____ hours.

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Detailed Solution

If a task can be completed by 45 people in 20 days, then 75 people will take 288 hours.
It is given that a task can be completed by 45 people in 20 days.
We know that two variables are said to be inversely proportional if and only if they are directly proportional to one another's reciprocal. If

x and y

are two variables in inverse variations, then

x ∝ 1 y ⇒ x = k 1 y ⇒ x = k y,        where k is proportianality constant ⇒ x y = k .... (1)

Let the time taken by 75 people is

x .

Since, on increasing the number of people, there will be a decrease in the number of days, therefore this is a case of inverse proportion. Thus,
We know that, 1 day = 24 hours.
Given that, 45 persons can complete a work in 20 days.
Therefore, the time taken by 1 person is: