A can complete a piece of work in 7 days and B can complete the same work in 12 days. A and B worked together for 3 days. C alone completed the remaining work in 9 days. How many days will C take to complete the same work entirely?

28

A = 7 days, B = 12 days,

⇒ A + B worked for 3 days = (12 + 7) x 3 = 19 x 3 = 57 units,   ..(Efficiency × Days = Total work)

⇒ Remaining work = 84 - 57 = 27 units,

⇒ C completed remaining units in 9 days = \(\frac{27}{C}\) = 9 days,

⇒ C = \(\frac{27}{9}\) = 3,  (Efficiency)

⇒ Time required by C to complete total work =  \(\frac{84}{3}\) = 28 days, ..(\(\frac{Work}{Efficiency}\) = Time)