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# $15$ persons complete a work in $4$ days by working $6$ hours a day. How many days will it take to complete the work if $5$ persons work the same hours per day?(a) $20$(b) $30$(c) $12$(d) $18$

Last updated date: 20th Jul 2024
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Hint: In order to determine the number of days it will take to complete the work if $5$ persons work the same hours per day. The amount of work done is equal to the amount of time it takes. and efficiency/one-day work/work rate removes the proportionally symbol. When the amount of work performed remains constant, efficiency is inversely proportional to the time taken.

Complete step-by-step solution:
In this problem,
As per the question given, the data are specifically noted as,
$\Rightarrow 15$ persons complete a work in $4$ days by working $6$ hours a day.
$\Rightarrow$ Similarly, calculate the number of days if $5$ persons work for the same hours per day.
We know that,
Number of persons is inversely proportional to the number of days.
And the number of hours is also inversely proportional to the number of days.
As per the solution,
$15$ persons working for $6$ hours a day = $15 \times 6 = 90$ hours for $4$ days.
$5$ persons working for $6$ hours a day = $5 \times 6 = 30$ hours
Now, we need to find the number of days as,
$\dfrac{{90}}{{30}} \times 4$ days $= 3 \times 4$ days
$= 12$ days
Thus, the number of days taken by $5$ persons to work for the same hours per day is $12$ days.
So as per the question we need to find the number of days for $5$ persons to work for $6$ hours a day.
Hence, $15$ persons complete a work in $4$ days by working $6$ hours a day.
It will take $12$ days to complete the work if $5$ persons work the same hours per day.
So, option (c) is the correct answer.

Note: Any task requires a specific amount of time.
Work is described as something that has an effect or produces a result, which is often the desired or anticipated result. The fundamental principle of Time and Work is the same as it is in all Arithmetic subjects, namely, proportionality.
Work completed equates to productivity and time spent.