A can do a piece of work in 12 days, B can do the same work in 8 days and c can do the same job in 4 / 5 th time required by both A and B. A and B work together for 3 days, then C complete days did C work?

As per question, work of A for 1 day = 1/12 and work of B for 1 day = 1/8
∴ Work of (A + B) together for 1 day = 1/12 + 1/8 = (2 + 3)/24 = 5/24
⇒ Work of (A + B) together for 3 days = 3 x (5/24) = 5/8
⇒ Remaining work after 3 days = 1 - 5/8 = 3/8
∵ C can do the same work in = 4/5th time required by (A + B) = 4/5 x 24/5 = 96/25 days
⇒ Work of C for 1 day = 25/96 part.
⇒ 25/96 part work can be done by C in 1 day
⇒ 3/8 part work can be done by C in = 96/25 x 3/8 days = 36/25 days = 1¹¹/₂₅
∴ The complete day C did the work = 1 day.