2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can do the same work in 8 days. In how many days can 2 men and 1 boy do the work?

ans is 8 or 12.5?

Question

2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can do the same work in 8 days. In how many days can 2 men and 1 boy do the work?

ans is 8 or 12.5?

vanessaperezxo · Answer

I think the answer would be 12.5

vanessaperezxo · Answer

because for it to be done in 8 day you need 3 men and 2 boys.. so if you have 2 men 1 boy it's going to take a few extra days. Do you get it? @yashiii

vanessaperezxo · Answer

@yashiii you there?

anonymous · Answer

yup....i think i solved it incorrectly .my ans was 8 ..hehhe

anonymous · Answer

@welshfella

vanessaperezxo · Answer

Oh ok, i have to go. Good luck solving the problem. sorry

anonymous · Answer

bye :) @vanessaperezxo

michele_laino · Answer

If I call with x the working rate of a man, and with y the working rate of a boy, then I can write this algebraic system:
$$\Large \left\{ \begin{gathered}
  2x + 3y = \frac{W}{{10}} \hfill \
  3x + 2y = \frac{W}{8} \hfill \ 
\end{gathered}  \right.$$
where W is the work to be done

phi · Answer

2 men and 3 boys can do a piece of work in 10 days 
2 men and 1 boy    will take longer (less help)
so if it's a choice between 8.5 and 12.5, pick 12.5

anonymous · Answer

a similar approach is to solve $$10(2x+3y)=1\
8(3x+2y)=1$$ which is not that elegant but works

anonymous · Answer

but as @phi said, common sense tells you it is longer than 8
it is in fact 12.5

anonymous · Answer

actually i want correct ans...those ans options were imaginary .:(

anonymous · Answer

how did you guess at the correct answer of 12.5?

anonymous · Answer

now i got ans 13.5 , so any one can pls tell me the accurate ans

anonymous · Answer

12.5 is correct

anonymous · Answer

@satellite73 , on any website someone solved it ,but other people were saying that ans is wrong. so m confused

anonymous · Answer

we can do it step by step, although i guess there probably a better method than i used

anonymous · Answer

put men's rate as x, boys at y
the first two statements translates as $$10(2x+3y)=1\
8(3x+2y)=1$$

anonymous · Answer

solving this for x and y gives $$x=\frac{7}{200},y=\frac{1}{100}$$

anonymous · Answer

@Michele_Laino , you have ne idea

anonymous · Answer

acha..okay..got it now :)

anonymous · Answer

oops i means solve $$T\left(\frac{14}{200}+\frac{1}{100}\right)=1$$

anonymous · Answer

and that gives $T=12.5$

anonymous · Answer

okay

michele_laino · Answer

I agree with @satellite73  we have to solve that system above, so we can find the requested time

anonymous · Answer

like i said, there may be a snappier way to do it, i don't know it

anonymous · Answer

@satellite73 , @Michele_Laino , thankyou so much both of you :)

michele_laino · Answer

:)