A can do a piece of work in 10 days. B can do it in 15 days. With the assistance of C they completed the work in 5 days. Find in how many days C alone can do it?

30

A = 10 days, B = 15 days,

⇒ According to the question, with assistance of C, A + B can complete the work in 5 days. 

⇒ \(\frac{30}{3 + 2 + C}\) = 5 days.          ..(\(\frac{Work}{Efficiency}\) = Time)

⇒ \(\frac{30}{5 + C}\) = 5, 

⇒ 30 = 25 + 5C 

⇒ 5C = 5

⇒ C = 1.  (Efficiency) 

⇒ Time required for C to do total work alone = \(\frac{30}{1}\) = 30 days