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2014-07-26T10:12:46+05:30

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10 days.
A, B , C can complete the work in a, b , c days respectively by working alone.
1/a + 1/b = 1/15      1/b + 1/c = 1/12      1/c + 1/a = 1/20
Add these equations :  2 [ 1/a + 1/b + 1/c ] = 1/15 + 1/12 + 1/20  = 1/5
     1/a + 1/b + 1/c = 1/10
A, B,C can do 1/10 work per day.  so 10 days to complete.
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2014-07-26T10:26:26+05:30
A+B= 15
B+C=12
C+A=20
A+B+C=?
SO,
ans is 5 days.
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