S₁ and S₂ can do a piece of work together in 18 days, S₂ and S₃ can do the same work together in 27 days, while S₃ and S₁ can do it together in 54 days. In how many days can all 3, working together, do 50% of the work ?

9 days

S1 + S2 = 18 days,

S2 + S3 = 27 days,

S3 + S1 = 54 days,

⇒ Adding all the efficiencies,

⇒ 2(S1 + S2 + S3) = 6,

⇒ S1 + S2 + S3 = 3,

⇒ Time required by S1 + S2 + S3 to complete 50% of total work = \(\frac{54/2}{3}\) = \(\frac{27}{3}\) = 9 days,  ..(\(\frac{Work}{Efficiency}\) = Time)