A and B, working together can finish a piece of work in 6 days, while A alone can do it in 9 days. How much time will B alone take to finish it?

Number of days A required do a piece of work : 9 days

Let number of days B required do a piece of work : X days

Number of hours required by A and B together to do a piece of work : 6 days

Work done by A in one day:

Work done by B in one day:

Work done by A and B together in a day :

Work done by A and B together in one day : = =

⇒ 6X + 54 = 9X

⇒ 3X = 54

⇒ X = 54/3 = 18

B can do the work 18 days