A and B can do a piece of work together in 10 days, B and C can do the same work together in 15 days, while C and A can do the same work together in 20 days. In how many days can A, B and C do the same work, working together ?

$\frac{120}{13}$ days

A + B = 10 days,

B + C = 15 days,

C + A = 20 days,

⇒ Adding all the efficiencies,

⇒ 2(X + Y + Z) = 13

⇒ X + Y + Z = \(\frac{13}{2}\),

⇒ Time required by A + B + C to complete the work = \(\frac{60}{13/2}\) = \(\frac{120}{13}\) days,     ..(\(\frac{Work}{Efficiency}\) = Time)