12. A and B can complete a certain job in 20 days
and 30 days respectively. They start the job
together and work for 3 days. Then B falls
sick and is unable to work for 5 days. During
this period A works alone. After this period, B
again join him
and they completed the work
together. In how many more days will the work
be completed?
Answers
Answer:
15 days.
Step-by-step explanation:
Method-1 Fraction Method
A completes the work in 30 days -> In 1 day he completes 1/30 part of job.
B completes the work in 20 days -> In 1 day he completes 1/20 part of job.
Work done by A & B both in 1 day= 1/30 + 1/20
=(20+30)/(20x30) = 5/60 = 1/12
Let both A & B workd for 'x' days.
Work done by them in x day = x/12
Remaining work = 1-x/12 ………(1)
This remaining work is done by A alone in 5 days.
Hence,
Work done by A in 5 days = Remaining work
5/30 = 1-x/12 …. From (1)
x/12 = 1–1/6
x = (5x12)/6
x=10
Total number of days to complete work = 10+5 = 15 days
Method-2 LCM Method
Let the total units of work be LCM(30,20)=60
A does 60/30 = 2 units per day work
B does 60/2 = 3 units per day work
Together they do (2+3)=5 units of per day work.
Let say both of them worked for x days.
Work done by them in x days = 5x
Remaining work = 60–5x
This remaining work done by A alone in 5 days
Hence,
5*(A's work per day)= 60–5x
5*2=60–5x
x=10
Total number of days taken to complete the work = 10+5 = 15 days
Method-3 Percentage Method
Let the total work be 100%
A does 100/30 = 3.33% work in 1 day
B does 100/20 = 5% work in 1 day
Both A & B do (3.33+5)=8.33% work in 1 day
Let say they worked for 'x' days
In x days the complete x*8.33% work.
Remaining work = 100%-x*8.33%
This remaining work completed by A alone in 5 days
Work done by A in 5 days = 5*3.33%= 16.66%
Hence,
Remaining work = work done by A in 5 days
100 - x*8.33%=16.66%
x*8.33% = 100%–16.66%
x*8.33% = 83.33%
x = 83.33/8.33
x=10 days
Total number of days taken to complete the work = 10+5 = 15 days