If a and b together can do a piece of work in x days, b and c together can do in y days and c and a together can do in z days, then the same work can be done
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work done by A and B in 1day =1/x
work done by B and C in 1day =1/y
work done by C and A in 1day = 1/z
Adding all the three,we get
2(A + B + C) in 1 day = 1/x +1/y +1/z
therefore A, B and C can together finish the work in
xy + yz + zx/ 2xyz
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