If A and B together can finish a piece of work in 12 days, Band C together can finish a piece of work in 15 days, C and A together ca finish a piece of work in 20 days. In how many days all three together finish the work? In how many days can each finish the same work alone?
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Answer:
Let A's 1 day work = a
B's 1 day work = b
C's 1 day work = c
∴A+B+C=121 ...(1)
A+C=2B ...(2)
A+B=3C ...(3)
From(2)
A=2B−C ...(4)
from (3)
A=3C−B ...(5)
comparing (4) and (5)
2B−C−3C−B
3B=4C
B=34C ...(6)
putting in (5)
A=BC−34C
A=35C ...(7)
putting (6) and (7) in (1)
35C+34C+C=121
312C=121
C=481
∴A=35×481=1445
B
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