Time & Work ( Part - 5)

Working Alternate Days

So far we have seen problems based on individual work, group work and working in pairs, and asked to find individual work or group work depending on the question. I hope that you people enjoying these posts and updating yourself. In this post iam providing stuff about the concept of people working alternate days.

Working alternate days means.... lets consider A and B are employed in a work and they are working alternate days. That means one day A is working and the other day B is working on the same work. And completes the work.

NOTE: It is important that who is starting the work.

Let's understand this concept by an example:

Q: A and B are employed to finish a work. A alone can complete the work in 10 days while B alone in 15 days. If they work on alternate days, starting with A, find the number of days taken to finish the job?

Sol:   Here A is working on 1st day. [A B A B A B A B ... This is the pattern]

          A ----  10          6

                            60 (Total work)

          B ----  15          4

  

Day - 1: A  does 6 work

Day - 2: B  does 4 work

i.e., in 2 days -----> 10 work is done

           2*6 days -----> 10*6 = 60 work

thus, 12 days required to complete the work.

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Q: A and B working separately can do a piece of work in 20 and 24 days. They work on alternate days starting with B on the first day. In how many days will the work be completed?

1. 23 days
2. 22 days
3. 21 (5/6) days
4. 21 days

Sol: A ---- 20             6

                         120

       B ---- 24             5

B is starting, B A B A B A B A ....

                     2 days ------ 11 work

       2*10 = 20days ------  11*10 = 110 work

Remaining work = 120 - 110 = 10

                    21st day B --- 5 work

              Remaining work is 10 - 5 = 5

This is done by A in 5/6 days (not a complete day).

 Hence, Total days = 21(5/6) days.

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Try this:

Q: A, B and C can do a work in 6, 10 and 8 days respectively, working individually. They started the work doing alternately. Find the number of days required to complete the work, if

(a) A started the work.

(b) B started the work.

(c) C started the work.

Post your answer in comment box below. Solution is provided soon...

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