A and B can do a piece of work in 12
days, B and C can do it in 15 days
and C and A can do the same work in
20 days. How long would A take to
complete the job?
Answers
A's 1 day work = 1/12 work
B's 1 day work = 1/15 work
C's 1 day work = 1/20 work
Total work = 1/12+1/15+1/20 = 12/60 = 1/5
They do total work in 5 days
A would take 12*5 = 60 days to complete
Answer:
30 days
Step-by-step explanation:
No of days taken by A and B to do the work = 12 days
No of days taken by B and C to do the work = 15 days
No of days taken by C and A to do the work = 20 days
SO,
Work done by A+B in 1 day = 1/12
Work done by B+C in 1 day = 1/15
Work done by C+A in 1 day = 1/20
Work done by (A+B) + (B+C) + (C+A) = 1/12 + 1/15 + 1/20
⇒(A+B) + (B+C) + (C+A) = 5 + 4 + 3 / 60
⇒(A+B) + (B+C) + (C+A) = 12/60 =1/5
⇒A + B + B + C + C + A = 1/5
⇒2A + 2B + 2C = 1/5
⇒2(A + B + C) = 1/5
⇒A + B + C = 1/10
∴Work done by A + B + C in 1 day = 1/10
Then, Work done by only A in 1 day
= A + B + C - B - C
= A + B + C - (B + C)
= 1/10 - 1/15
= 1/30
∴Work done by A in 1 day = 1/30
∴A can do the whole work in 30 days.
I HOPE THIS HELPS.
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