A and B can do a piece of work in 12 days. B and C together do it in 15 days. If A is twice as good a workman as C, find in what t

A and B can do a piece of work in 12 days. B and C together do it in 15 days. If A is twice as good a workman as C, find in what time B will alone do it?

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  1. Given:-

    •A and B can do a piece of work in 12 days.

    •B and C together do it in 15days.

    •A is twice as good a workman as C.

    To Find:-

    •What time B will alone do it.

    Solution:-

    Let consider work done by C be x and work done by A be 2x.

    According to the question,

    [tex] \:  \:  \sf \:  \frac{1}{x}  –  \frac{1}{2x}  =  \frac{1}{60}  \\  \\  \:  \:   \sf \:  \frac{2 – 1}{2x}  =  \frac{1}{60}  \\  \\  \:  \:  \sf \:  \frac{1}{2x}  =  \frac{1}{60}  \\  \\  \:  \:  \sf \: x = 30…(i)[/tex]

    Hence, the value of x is 30.

    B’s 1 days work

    [tex] \:  \:  \sf \:  =  \frac{1}{12}  –  \frac{1}{30} (from \: equation \: (i)) \\  \\  \:  \:  \sf \:  =  \frac{5 – 2}{60}  =  \frac{3}{60}  =  \frac{1}{20} [/tex]

    Hence,B alone will complete the work in 20 days.

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