Question

A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will do it in :

Answer 1

Let A complete the whole piece of work in A days. It means that in one day A can do (1/A) amount of work.
Similarly, B can do (1/B) amount of work in one day and C can do (1/C) amount of work in one day.

When A and B work together, work is finished in 8 days.

(no of days)×(amount of work done by A in 1 day) + (no of days)×(amount of work done by B in 1 day) = 1 {1 means that they have completed the whole work, that's why its not a fractional quantity}

8(1/A)+8(1/B)=1
(1/A)+(1/B)=1/8 ---1

Similarly,
(1/B)+(1/C)=1/12 ---2
and
(1/A)+(1/B)+(1/C)=1/6 ---3

Let us consider that A and C together completes the work in x days. Therefore, similarly,
(1/A)+(1/C)=1/x ---4

add eq 1, 2 and 4, you will get,

2(1/A+1/B+1/C) =1/8+1/12+1/x
2(1/6)=1/3 =1/8+1/12+1/x

Now solve this,

1/x = 1/3-1/8-1/12 = (8-3-2 ) /24= 3/24= 1/6

x=6 days
Therefore A and C can complete the work together​ in 6 days.