B alone can finish the work in how many days?

Question

A takes twice as much as time as B or thrice as much as time as C. Working together they can finish the work in 6 days. B alone can finish the work in how many days

Answer 1

18 days

Answer 2

If A completes the work in A days, B in B days and C in C days. A=2B=3C. If they work together the following equation applies: 1/A+2/A+3/A=1/6. Multiply through by 6A: 6+12+18=A, so A=36 days and B=36/2=18 days.

Explanation: if it takes 6 days to complete the work, then 1/6 of the work is done in one day. If A takes A days to complete the work, then in one day 1/A of the work will be done. Similarly for B and C. So the equation shows how the three workers combine to do a sixth of the work in a day. B=A/2 and C=A/3 so 1/B=2/A and 1/C=3/A.