A given work can be done by Amar in 10 days, by Akbar in 20 days and Antony in 40 days. Amar starts the work on the first day and Akbar follows it on
the second day and Antony on the third day. They continue to do this in rotation until the job is completed. The number of days it takes to complete the
work is :
Answers
Given:
Amar does the work in 10 days
Akbar does the work in 20 days
Antony does the work in 40 days
To find:
The number of days taken to complete the work.
Solution:
The amount of work that Amar can do in one day = 1/10
For Akbar = 1/20
For Antony = 1/40
Since they all work in rotation for a day:
The amount of work they can do in 3 days will be = 1/10 + 1/20 + 1/40 =7/40
Up till the next 3 days they would complete 14/40 amount of work and so on.
Let the total work done be W
The work completed at the end of each 3 days will be:
7/40*W - after 3 days
14/40*W - after 6 days
21/40*W - after 9 days
28/40*W - after 12 days
35/40*W - after 15 days
Work left after 15 days = W - 35/40 = 5/40
When Akbar does his work, work left after he did his work after 16 days = (1/8 - 1/10) W= 1/40W
Akbar can complete the rest if the work and there will be no need of Antony to work.
Since Akbar can do 1/20 amount of work in 1 day,
He can do 1/40 amount of work in 1/2 days.
Total days = 15 + 1 + 0.5 = 16.5 days
Therefore, they would take 16.5 days to complete the work.
Given : given work can be done by Amar in 10 days, by Akbar in 20 days and Antony in 40 days .
Amar starts the work on the first day and Akbar follows it on
the second day and Antony on the third day. They continue to do this in rotation until the job is completed.
To Find : The number of days it takes to complete the work
Solution:
Amar 1 day work = 1/10
Akbar 1 day work = 1/20
Anthony 1 day work = 1/40
Total 1 Day work together = 1/10 + 1/20 + 1/40
= (4 + 2 + 1) /40
= 7/40
As they do in rotation one at a time so 3 Days work = 7/40
1/(7/40) = 40/7 > 5
Hence Work Done in 5 x 3 = 15 Day
= (7/40)*5 = 7/8
Work Left = 1 - 7/8 = 1/8
Work Done on 16th Day by Amar = 1/10
Work Left = 1/8 - 1/10
= (5 - 4)/40
= 1/40
1/40 work done by Akbar in (1/40)/(1/20) = 1/2 Days
Hence Total Number of Days taken to complete the task
= 15 + 1 + 0.5
= 16.5 Days
Work will be completed in 16.5 Days.
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