14 typists typing 6 hours a day can take 12 days to complete the manuscript of book . How many days will 4 typists, working 7hours a day,can take to do the same job ?
Answers
36 days
Here the 14 typists need 12 days to complete the manuscript of a book if they're working for 6 hours per day. Well, first we have to find the total time taken by them for completing the manuscript.
Well, it's simply,
Total time consumed for the work = No. of days × Time consumed per day.
Here the total time consumed should be the same in that of the time consumed per day, i.e., in hours. If the time needed per day was in minutes, then so would be the total time needed.
So the 14 typists need 12 × 6 = 72 hours in total for completing the manuscript of the book.
Now, without loss of generality, we can say that the no. of workers for completing a particular job is inversely proportional to the time taken by them for completing the job. It can be simply understood that as the no. of typists increases, then the work can easily be completed taking less time, and vice versa.
Here 14 typists need 72 hours in total for completing the manuscript of the book. So the constant of proportionality is 14 × 72 = 1008 hours. This means that a typist can alone complete the manuscript in 1008 hours.
Well, the time needed for 4 typists to complete the manuscript will be, 1008 / 4 = 252 hours, in total.
We can say that,
No. of days needed for the 4 typists typing an hour per day = 252 days.
Keep in mind that the rate of job (time consumed per day) is also inversely proportional to the total no. of days needed for them. Here, in this case, the constant of proportionality is 252.
Thus we get that,
No. of days needed for the 4 typists typing 7 hours per day = 252 / 7 = 36 days.
Hence 4 typists typing 7 hours a day take 36 days to complete the manuscript of the book.
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