A and B can complete a piece of work in 27 days and 54 days, respectively. They completed the work in 9 days with the help of C. How many days will C take to complete eight-ninths of the work alone?

16

A = 27 days, B = 54 days,

⇒ With the help of C, A + B can complete the work in 9 days = \(\frac{54}{2+1+C}\) = 9 days,

⇒ \(\frac{54}{3+C}\) = 9 days,   

⇒ 54 = 27 + 9C

⇒ 27 = 9C

⇒ C = 3,   (Efficiency)

⇒ Time required by C to complete 8/9th of the work = \(\frac{8/9 * 54}{3}\) = \(\frac{48}{3}\) = 16 days,  ..(\(\frac{Work}{Efficiency}\) = Time)