A can complete one-third of a work in 5 days and B can do $\frac{2}{5}$th of the same work in 10 days. They work together for 6 days. The remaining work is completed by C in 18 days. C alone will do the same work in:

50 days

A = \(\frac{1}{3}\)W = 5 days = 15 days,

B = \(\frac{2}{5}\)W = 10 days = 25 days,

⇒ A + B worked for 6 days = (5 + 3) x 6 = 8 x 6 = 48 units,   ..(Efficiency × Days = Total work)

⇒ Remaining work = 75 - 48 = 27 units,

⇒ C completes the remaining work in 18 days = \(\frac{27}{C}\) = 18 days,

⇒ C = \(\frac{27}{18}\) = \(\frac{3}{2}\)  (Efficiency)

⇒ Time required by C to complete the work alone = \(\frac{75}{3/2}\) = 50 days,    ..(\(\frac{Work}{Efficiency}\) = Time)