A, B and C can alone do a task in 40, 120 and 36 days respectively. A and B together work for 20 days and leave the task incomplete. C resumes it and completes it alone. How many days did C take to complete it?

12

A = 40 days, B = 120 days, C = 36 days,

⇒ A + B worked for 20 days = (9 + 3) x 20 = 12 x 20 = 240 units,  ..(Efficiency × Days = Total work)

⇒ Remaining work = 360 - 240 = 120 units,

⇒ Remaining work is completed by C alone = \(\frac{120}{10}\) = 12 days.   ..(\(\frac{Work}{Efficiency}\) = Time)