A, B&C alone can complete a piece of work in 20,30,40 days respectively. if they start working alternatively each days and A start first. find at which work will be completed
Answers
Answer:
24 days
Step-by-step explanation:
Assuming you forgot to write the word "day" in the last line -
A can do the job in 20 days. That is he does 1/20 of the job in a day.
B can do the job in 30 days. That is he does 1/30 of the job in a day.
The LCM of 20 and 30 is 60. Hence A does 3/60 of the job in a day while B does 2/60 of the job in a day.
Let us assume that A starts to do his part on the first day. At the end of the day he has completed 3/60 th of the job. what remains is 57/60.
On the second day B does 2/60 th of the job and what remains at the end of the second day is 57/60 - 2/60 = 55/60 th of the job.
On the third day A does 3/60 th of the job and what remains at the end of the third day is = (55 - 3)/60 = 52/60 th of the job.
On the fourth day B does 2/60 th of the job and what remains at the end of the second day is = (52 - 2)/60 = 50/60 th of the job.
On the fifth day A does 3/60 th of the job and what remains at the end of the third day is = (50/60 - 3/60) = 47/60 th of the job.
On the sixth day B does 2/60 th of the job and what remains at the end of the third day is = (47/60 - 2/60) = 45/60 th of the job.
So you see a pattern forming. The numerator reduces by 3 when A finishes his part of the job on a particular day and it reduces by 2 when B finishes his part of the job on a particular day. The denominator remains 60 right through. So continuing int he same manner:
At the end of 7th day A finishes his work and the balance is 42/60 th.
At the end of 8th day B finishes his work and the balance is 40/60 th.
At the end of 9th day A finishes his work and the balance is 37/60 th.
At the end of 10th day B finishes his work and the balance is 35/60 th.
At the end of 11th day A finishes his work and the balance is 32/60 th.
At the end of 12th day B finishes his work and the balance is 30/60 th.
At the end of 13th day A finishes his work and the balance is 27/60 th.
At the end of 14th day B finishes his work and the balance is 25/60 th.
At the end of 15th day A finishes his work and the balance is 22/60 th.
At the end of 16th day B finishes his work and the balance is 20/60 th.
At the end of 17th day A finishes his work and the balance is 17/60 th.
At the end of 18th day B finishes his work and the balance is 15/60 th.
At the end of 19th day A finishes his work and the balance is 12/60 th.
At the end of 20th day B finishes his work and the balance is 10/60 th.
At the end of 21st day A finishes his work and the balance is 7/60 th.
At the end of 22nd day B finishes his work and the balance is 5/60 th.
At the end of 23rd day A finishes his work and the balance is 2/60 th.
At the end of 24th day B finishes his work and the balance is 0/60 th.
Hence with A and B working on alternate days, the entire job gets completed in 24 days.