Question

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?

Answer 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,

$\:  \:  \sf \:  \frac{1}{x}  -  \frac{1}{2x}  =  \frac{1}{60}  \\  \\  \:  \:   \sf \:  \frac{2 - 1}{2x}  =  \frac{1}{60}  \\  \\  \:  \:  \sf \:  \frac{1}{2x}  =  \frac{1}{60}  \\  \\  \:  \:  \sf \: x = 30...(i)$

Hence, the value of x is 30.

B's 1 days work

$\:  \:  \sf \:  =  \frac{1}{12}  -  \frac{1}{30} (from \: equation \: (i)) \\  \\  \:  \:  \sf \:  =  \frac{5 - 2}{60}  =  \frac{3}{60}  =  \frac{1}{20}$

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