To calculate time to complete a work in general if a person A completes 1/n th part of work in one day, then the time taken by A to complete the work = n days.
If a man takes 10 days to complete a piece of work; then according to the unitary method work done in a 1 day = 1/10. On the other hand, if a man completes 1/10th of the work in one day, to complete the work he will takes 10 days.
Now we will apply the concept of solving some real-life problems to find the time required to complete a piece of work.
Solved examples to calculate time to complete a work:
1. David can do a piece of work in 2 days while Ron can do the same work in 5 days. How long will it take if both of them work together?
Time taken by David to do the work = 2 days
Work done by David in 1 day = 1/2
Time taken by Ron to do the work = 5 days
Work done by Ron in 1 day = 1/5
So, work by David and Ron in one day = 1/2 + 1/5
= (5 + 2)/10
Therefore, David and Ron can do a piece of work in 10/7 days, i.e., 1 3/7 days.
2. X can do a piece of work in 15 days while Y can do it in 30 days. If both of them at it together, in how many days will they be able to finish the work?
Time taken by X to do a piece of work = 15 days
X’s one day’s work = 1/15 days
Time taken by Y to do a piece of work = 30 days
Y‘s one day’s work = 1/30 days
(X + Y)‘s one day’s work = 1/15 + 1/30
= (2 + 1)/30
Therefore, both of them can finish the work in 10 days.
3. Harry and Sam can together plough the field in 5 days. Harry alone takes 8 days to plough the same field. In how many days can Sam alone plough the field?
Time taken by Harry and Sam to plough the field together = 5 days
Therefore, Harry’s and Sam’s one day’s work = 1/5
Time taken by Harry to plough the field = 8 days.
Therefore, Harry’s one day’s work = 1/8
Therefore, Sam’s one day’s work = 1/5 – 1/8
= (8 – 5)/40
Therefore, Sam can plough the
field in 3/40 days.
4. Aaron and Brandon can together do pieces of work in 15 days. Aaron alone can finish it in 20 days. How many days will Brandon take to finish the same work?
(Aaron + Brandon)’s one day’s work = 1/15
Aaron’s one day’s work = 1/20
Therefore, Brandon’s one day’s work = (Aaron + Brandon)’s one day work – Aaron’s one day work
= 1/15 – 1/20
= (4 – 3)/60
Brandon alone can finish the work in 60 days.