Question 1034185
.
Plz solve:

3 men and 18 children together take 2 days to complete a piece of work. 
How many days will 18 children alone take to complete the piece of work, 
if 6 men alone can complete the piece of work in 3 days?
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<pre>
Let m be the man's   rate of work, in terms of {{{job/day}}}, and
let c be the child's rate of work, in the same terms.

Then from the condition you have this system of equations

3m + 18c = {{{1/2}}},   (1)
6m       = {{{1/3}}}.   (2)

From (2), m = {{{1/(3*6)}}} = {{{1/18}}}.

Substitute it into (1). You will get

{{{3/18}}} + 18c = {{{1/2}}}  --->  {{{1/6}}} + 18c = {{{1/2}}}  --->  18c = {{{1/2 - 1/6}}} = {{{2/6}}} = {{{1/3}}}.

Hence,  c = {{{1/(3*18)}}} = {{{1/54}}}.

This is rate of work of one child.

So, 18 children will complete  {{{1/3}}}  of the job in one day, and
it will take 3 days for them to complete the job.

<U>Answer</U>. 3 days.
</pre>