A and B together can complete a task in 10 days, B and C can do in 15 days, and C and A together can do it in 12 days. How long will they take to complete the task working together?

A and B together can complete a task in 10 days. B and C can do it together in 15 days. C and A together can do it in 12 days LCM of 10, 15 and 12 is 60 ⇒ The total task is 60 units. In 1 day A and B together can do 60/10 = 6 unit task In 1 day B and C can do together 60/15 = 4 unit task In 1 day C and A can do together 60/12 = 5 unit task In 1 day (A + B + B + C + C + A) can do (6 + 4 + 5) = 15 unit task ⇒ 2(A + B + C) can do 15 unit task in 1 day ⇒ (A + B + C) can do 15/2 = 7.5 unit task in 1 day Together A, B and C will take time to do the task (60/7.5) = 8 days. ∴ They will take 8 days to complete the task together.