Answer:
Option C
Explanation:
$12$ children take $16$ days to complete the work.
$\Rightarrow$ $1$ child takes $16\times 12=192$ days to complete the work.
$\Rightarrow$ Work done by $1$ child in $1$ day $=\frac{1}{192}$
$8$ adults take $12$ days to complete the work.
$\Rightarrow$ $1$ adult takes $12\times 8=96$ days to complete the work.
$\Rightarrow$ Work done by $1$ adult in $1$ day $=\frac{1}{96}$.
$16$ adults worked for $3$ days
Work completed $=16\times\frac{1}{96}\times 3$ $=\frac{1}{2}$.
Remaining work $=1-\frac{1}{2}$ $=\frac{1}{2}$
The remaining work is done by $6$ adults and $4$ children
Work done in $1$ day $=6\times\frac{1}{96}+4\times\frac{1}{192}$ $=\frac{1}{16}+\frac{1}{48}$ $=\frac{1}{12}$.
Required days to complete the remaining work $=\frac{1}{2}\div\frac{1}{12}$ = 6 days.
