If A and B together can complete a work in 18 days, A and C together in 12 days and B and C together in 9 days, then B alone can do the work in ____?

If A and B together can complete a work in 18 days, A and C together in 12 days and B and C together in 9 days, then B alone can do the work in ____?

Explanation

Using the concept of work and rate, we can analyze the given information:

A+B = 1/18 (work done per day)

A+C = 1/12

B+C = 1/9

By adding the first two equations, we get:

(A+B) + (A+C) = 1/18 + 1/12

2A + (B+C) = 1/6

2A + 1/9 = 1/6

2A = 1/6 - 1/9

2A = 1/18

A = 1/36 (work done by A per day)

Now, we can find B's work per day:

B = 1/18 - 1/36 = 1/24

So, B alone can do the work in 24 days.