# A and B Together can Complete a Piece of Work

A and B together can complete a piece of work in 8 days while B and C together can do it in 12 days. All the three together can complete the work in 6 days. In how much time will A and C together complete the work?

- 8 days
- 10 days
- 12 days
- 20 days

**Answer: (1) 8 days**

**Explanation:-**

A and B together can complete a piece of work = 8 days

A and together can do work in a day = 1/8 day

B and C can do complete same work = 12 days

B and C can do work in a day = 1/12 day

All the three together can complete the work = 6 days

All the three together can do work in a day = 1/6

A and C can do work in a day = 2 x 1/6 – ( 1/8 + 1/12)

= 1/3 – 5/24

= (8 – 5)/24

= 3/24 = 1/8

All the three together can do a piece of work = 8 days

Hence, the answer is (1) 8 days.