A and B can do a work in 12 days, B and C can do it in 15 days and C and A can do it in 20 days. If A, B and C work together, then they will complete the same work in :

10 days

A + B = 12 days,

B + C = 15 days,

C + A = 20 days,

⇒ Adding all the efficiencies,

⇒ 2(A + B + C) = 12,

⇒ A + B + C = 6,

⇒ Time required by A + B + C to complete the work = \(\frac{60}{6}\) = 10 days,    ..(\(\frac{Work}{Efficiency}\) = Time)