Question

$16$ men can complete a work in $12$ days, $24$ children can complete the same work in $18$ days, $12$ men and $8$ children started working and after $8$ days, $3$ more children joined them. How many days will they now take to complete the remaining work ?

• A. $2$ days
• B. $4$ days
• C. $6$ days
• D. $8$ days

Answer 1

The correct option is B $4$ days

One day work of 16 men is $\frac{1}{12}$.

One day work of 24 children is $\frac{1}{18}$.

One men's one day work is $\frac{1}{12\times 16}$.

One child's one day work is $\frac{1}{24\times 18}$.

One day work of 12 men and 8 children is $\frac{12}{12\times 16}+\frac{8}{24\times 18}$.

One day work = $\frac{35}{54\times 8}$.

Work done in 8 days = $8\times \frac{35}{54\times 8}=\frac{35}{54}$.

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

The remaining work is 12$\times$ one men's one day work + 11$\times$ one child's one day work.

Hence, $12\times \frac{1}{12\times 16}+11\times 24\times 18$

One day work multiplied by number of days to complete remaining work = remaining work

Therefore, the work is done in 4 days.

$(\frac{1}{16}+\frac{11}{24}\times 18)x=\frac{19}{54}$

$\Rightarrow$$x=4$

Thus they take 4 days to complete the remaining work.

Hence option B is correct.