Discussion Forum

Sixteen men can complete a work in twelve days. Twenty-four children can complete the same work in eighteen days. Twelve men and eight children started working and after eight days three more children joined them. How many days will they now take to complete the remaining work ?

Answer:

Explanation:

$1$ man's $1$ day work $=\frac{1}{192}$

child's $1$ day's work = $\frac{1}{432}$.

Work done in $8$ days $=8\left(\frac{12}{192}+\frac{8}{432}\right)$ $=8\left(\frac{1}{16}+\frac{1}{54}\right)$ $=\frac{35}{54}$.

Remaining work $=1-\frac{35}{54}$ $=\frac{19}{54}$.

($12$ men $+11$ children)'s $1$ day work $=\frac{12}{192}+\frac{11}{432}$ $=\frac{19}{216}$.

Now, $\frac{19}{216}$ work is done by them in $1$ day.

$\therefore\frac{19}{54}$ work will be done by them in $\left(\frac{216}{19}\times\frac{19}{54}\right)$ = 4 days.