C can do a work alone in 120 days. B is twice as efficient as C and A is thrice as efficient as B. In how many days can they together complete the work?

13.33

C = 120 days,

According to the question,

         A  :  B  :  C

⇒      3  :  1

⇒          :  2  :  1

⇒     6  :  2  :  1      (Efficiency)

⇒ Total work = 1 x 120 days = 120 units,    ..(Efficiency × Days = Total work)

⇒ Time required by A + B + C to complete the total work = \(\frac{120}{6+2+1}\) =  \(\frac{120}{9}\) = 13.33 days   ..(\(\frac{Work}{Efficiency}\) = Time)