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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## 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.