Twelve children take sixteen days to complete a work which can be completed by 8 adults in 12 days. After working for 3 days, sixteen adults left and six adults and four children joined them. How many days will they take to complete the remaining work ?

12 children take 16 days to complete a work.

so,

1 child’s 1 day’s work=1/(12*16)

1 child’s 1 day’s work=1/192

8 adults take 12 days to complete a work.

So, 

1 adult’s day’s work=1/(8*12)

1 adults day’s work=1/96

But, after working of 3 days, 16 adults left

so, 

16 adults 3 day’s work= 16*3*1/96

16 adults 3 day’s work=1/2

therefore,

the remaining work will be:

Remaining work=1-1/2

Remaining work=1/2

Now (6 adults+ 4 Children) 1 day’s work will be:

(6 adults+4 children) 1 day’s work=6/96+4/192

(6 adults+4 children) 1 day’s work= 16/192

(6 adults+4 children) 1 day’s work=1/12

so,

1/12th of the work is done by them in 1 day

thus,

they take following days to complete the remaining work.

(1÷1/12)*1/2

(1*12)*1/2

12/2

6 days