Question

12 Children take 16 days to complete a work which can be completed by 8 adults in 12 days. 16 adults started working and after 3 days, 10 adults left and 4 children joined them. How many days will it take them to complete the remaining work ?

• A. 4
• B. 5
• C. 6
• D. 7

Answer 1

The correct option is C 6

12 children take 16 days to complete a work.

So, 1 child's 1 days' work $=\frac{1}{12\times 16}=\frac{1}{192}$

8 adults take 12 days to complete a work.

So, 1 adult's days' work $=\frac{1}{8\times 12}=\frac{1}{96}$

16 adults' 3 days' work $=16\times 3\times \frac{1}{96}=\frac{1}{2}$

Remaining work $=1-\frac{1}{2}=\frac{1}{2}$

Now (6 adults' + 4 children's) 1 days' work $=\frac{6}{96}+\frac{4}{192}=\frac{16}{192}=\frac{1}{12}$

$\therefore \frac{1}{12}th$ of the work is done by them in 1 day

$\therefore \frac{1}{12}$ of the work will be done in $\frac{1}{1/12}\times \frac{1}{2}$ days = 6 days