A and B together can complete a work in 20 days. B and C together can complete the same work in 15 days. If A, B and C all work together, then the same work gets completed in 10 days. How many days will A and C together take to complete the same work?

12 days

A + B = 20 days,

B + C = 15 days,

A + B+ C = 10 days,

⇒ Solving above equation we get individual efficiencies,

⇒ A : B : C = 2 : 1 : 3

⇒ Time taken by A + C to complete total work is = \(\frac{60}{2+3}\) = \(\frac{60}{5}\) = 12 days.     ..(\(\frac{Work}{Efficiency}\) = Time)