Twelve children take sixteen days to complete a work which can be completed by eight adults in twelve days. Sixteen adults started working and after three days ten adults left and four children joined them. How many days will they take to complete the remaining work ? 3 b. 4 c. 6 d. 8 e. none of these

First, let's find the relationship between the work done by the children and the adults.

We know that 12 children can complete the work in 16 days and 8 adults can complete the same work in 12 days. So, we can say that the work done by 12 children in 1 day is equal to the work done by 8 adults in 1 day.

Let's denote the work done by 1 child in 1 day as C and the work done by 1 adult in 1 day as A. So, we have:

12C = 8A

Now, let's find the work done by 16 adults in 3 days:

16 adults * 3 days = 48A

After 3 days, 10 adults left and 4 children joined. So, we have 6 adults and 4 children working. Let's denote the remaining work as R. We have:

R = (6A + 4C) * days

We know that 12C = 8A, so we can substitute C with (2/3)A in the above equation:

R = (6A + 4*(2/3)A) * days R = (6A + 8/3A) * days R = (26/3A) * days

We know that the total work is equal to the work done by 16 adults in 3 days plus the remaining work:

48A + R = total work

Substituting R with (26/3A) * days in the above equation:

48A + (26/3A) * days = total work

We know that the total work is also equal to the work done by 8 adults in 12 days:

8A * 12 days = total work

So, we have:

48A + (26/3A) * days = 8A * 12 days 48A + (26/3A) * days = 96A (26/3A) * days = 96A - 48A (26/3A) * days = 48A days = (48A * 3) / 26A days = 144 / 26 days = 5.54

So, the remaining work will be completed in approximately 6 days. Therefore, the answer is c. 6.