0
$\begingroup$

A can do the work in 15 days and B can demolish that work in 20 days. If they work on alternate day starting with A, how many days are required to do the work?

Total unit of work= LCM(15,20)=60 units A can do 4 units B= -3 units( - because B demolishes the work) Now, in 2 days 1 unit work will be completed. I understood till this point. Now, in the solution it has been given that subtract the maximum work from 60 which gives us 56. 1 unit-2days 56 units-112 days hence, total number of days is 113. Help me understand this solution.

  • 1
    The last 4 units done by A the last day aren't going to be demolished because the work is done, that's why they are subtracted. – 2017-02-12
  • 0
    What an odd question. It asks how many days are *required* which connotes the minimum possible number of days to complete the work with the available resources. The minimum is achieved by having B take a vacation (it says "B can demolish", not "B will demolish"), allowing A to complete the work in 15 days. – 2017-05-19

2 Answers 2

2

The last few days of work take us close to completing the $60$ units of work. After $112$ days $56$ units have been completed, which is one day's worth of work by $A$ short of completion. And since $112$ is even, the next day is indeed $A$'s day to work and she can complete the project.

enter image description here

  • 0
    If it would have been for three people then? – 2017-02-12
  • 0
    A did work in 12 days and B in 20 days and suppose C demolishes it in 15days. So in 3 days it will complete 4 units of work. But how we will know who will work on the last date? – 2017-02-12
  • 0
    Since A and C both work on odd days. @Joffan – 2017-02-12
  • 0
    @CoderSingh You would have to specify the working order of participants and also work out which day of the cycle had the most-advanced work status. I suggest you accept whichever answer here helped you most (click the check mark on one answer) and then ask another question to get a proper answer to that. – 2017-02-12
0

As you say, the "net effect" of two days is one unit. Hence after 112 days, 56 units will be completed. You may think that 57 units are completed after 114 days, 58 after 116 days, 59 after 118 days, and finally all 60 after 120 days. But that would ignore that the constructive work done by A on day 113 already takes us to the final 60 units (for the first time).

  • 0
    But my question is why we assumed it to be 56 units. Why we didn't solve this question by taking 60 units itself? Why we have subtracted 4 units? – 2017-02-12
  • 0
    My answer according to me is 120 days @HagonvonEitzen – 2017-02-12