A and B do a work in 20 days and
12 days respectively. A started the work after 4 days B join him. The work completed is how many day .
Answers
Step-by-step explanation:
A and B can do a piece of work in 20 days and 12 days respectively. A started the work alone then after 5 days, ‘B’ joined him till the completion of the work. How long did the work last?
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Given,
A can do a work in 20 days.
=> In a single day, A will complete 1/20th part of the total work.
B can do a work in 12 days.
=> In a single day, B will complete 1/12th part of the total work.
So, if they both work together,
=> 1/20 + 1/12
=> 3/60 + 5/60
=> 8/60
=> 2/15
In a single day, A and B together will complete 2/15th part of the total work.
Now, let's move forward to what other things are given. A already worked for 5 days. So, the amount of work completed is
=> 5*(1/20)
=> 1/4.
As 1/4th of the work is already completed so now A and B have to complete the rest 3/4th of the work together.
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Let A & B work together for d days.
A works for 5 + d days and B works for d days only.
=> (5 + d)/20 + d/12 = 1
=> 60 + 12d + 20d = 240
=> d= 180/32 = 5 5/8 days
Total number of days = 10 5/8 days
Another method :
Let total work = LCM(12,20) = 60 units
A's ones day work = 3 units
B's one day work = 5 units
In 5 days, A completes 15 units.
Remaining 45 units will be completed by both A & B together in 45/(3+5) = 5 5/8 days.
Total days = 5 + 5 5/8 = 10 5/8 days
Check :-
In 10 5/8 days, A will complete :
85/8 x 1/20 work
In 5 5/8 days, B will complete:
5 5/8 x 1/12 work
Total work :
85/8 x 1/20 + 5 5/8 x 1/12 = 1
Answer: