Question

A can do a work in 30 days, B in X days, C can destroy the work in 50 days. If A and B work together alternating with C, they complete the work in 355/7 days. How long will it take for B to complete the work alone?

Answer 1

You can do a work in 30 days, or 1/30th of the work per day. B takes x days, of 1/x of the work per day. C destroys the work at a rate of 1/50th per day. So, you have:
1/30 + 1/x -1/50=1/(355/7) or 7/355
1/75+1/x=7/355
525/26625-355/26625=1/x
170/26625=1/x
170x=26625
x=5325/34 days for B to finish the work alone.
☺☺☺☺