A can work in one hour 1/4 of work.
B&C  in one hour can do 1/3 of work
A&C  in hour can do 1/2 of work
C in one hour produces= (1/2)-1/4=1/4 work
 ⇒ B in one hour produces=(1/3)-1/4 =1/12 work
Hence B will take 1/(1/12) = 12 hours to complete work.
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     A can do  1/4 th of work in 1 hour
     B + C can do 1/3 rd of work in 1 hour
     A + C  can do 1/2 of work in 1 hour

    A+ B + C  can do  1/4+1/3 of work in 1 hour,  ie.,  7/12 th of work in  1 hour
     So B can do what (A+B+C) do  -  what (A+C) do in 1 hour
             ie.,  7/12 - 1/2
                = 1/12 th of work in 1 hour

     hence B will do  work in 12 hours.

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