Question

8 men working for 9 hours a day can complete a piece of work in 20 days. In how many days can 7 men working for 10 hours a day complete the same piece of work ?
A. \[20\dfrac{1}{2}\]
B. \[20\dfrac{3}{5}\]
C. \[21\]
D. \[20\dfrac{4}{7}\]

Answer 1

Hint: Let us find work done by each man in one hour. And to find the total work that has to be done after that we can find that in how many days work will be finished. As we know that it is given in the question that when there are 8 men and they work for 9 hours a day then the work will be finished in 20 days.

Complete step-by-step solution:
So, let the work done by each man in one hour be x.
So, according to the above given condition.
Work done by 8 men in one hour will be equal to 8x.
Each day they work for 9 hours.
So, work done by all man in one day will be 9*8x = 72x.
As we know that they take 20 days to finish the work.
So, total work will be 20*72x = 1440x.
Now we have to find time taken by 7 men to complete the work if they work 10 hours a day.
Let the total days it takes to complete the work when there were 7 men be t days.
So, as we know that each man does x work in one hour a day.
So, work done by 7 men in one hour will be 7x.
And work done by these seven men in 10 hours will be 10*7x = 70x.
So, work done in t days will be 70x*t = 70xt.
As we know that total work is 1440x.
So, 1440x = 70xt
Now dividing both sides of the above equation by 70x. We get,
t = \[\dfrac{{144}}{7}\] days = \[20\dfrac{4}{7}\] days.
So, the same piece of work will be finished in \[20\dfrac{4}{7}\] days if there are 7 men and each man works 10 hours a day.
Hence, the correct option will be D.

Note: As the total work that has to be done in both the cases is the same and work done by each man in one hour is the same. So, first, we assume that the total days will be t and then find the work done by 8 men if they work 9 hours a day and work for 20 days. And then find the work done by 7 men if they work for 10 hours a day and work for t days and then equate the work done in both the cases to get the required value of t. This will be the easiest and efficient way to find the solution of the problem.