Chemerical71 wrote:

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 man and 1 boy do the work?

A. 15

B. 18

C. 12.5

D. 10

E. 16

Two points before coming to the solution..

1) under no circumstances, it is sub-600 level.

2) the choices are always in ascending order, so may not be a very authentic source although the Q is ok.

Let m men can complete the job on their own and B boys can complete the work.

So \(\frac{2}{m}+\frac{3}{b}=\frac{1}{10}\)..

\(\frac{2*3}{m}+\frac{3*3}{b}=\frac{3}{10}\)..(i)

\(\frac{3}{m}+\frac{2}{b}=\frac{1}{8}\)...

\(\frac{2*3}{m}+\frac{2*2}{b}=\frac{2}{8}\)...(ii)

Subtract i from ii..

\(\frac{9}{b}-\frac{4}{b}=\frac{3}{10}-\frac{2}{8}\)..

\(\frac{5}{b}=\frac{1}{20}\)...

Or b=20*5=100..

Substitute in i to get value of m..

\(\frac{2}{m}+\frac{3}{100}=\frac{1}{10}\)..

\(\frac{2}{m}=\frac{1}{10}-\frac{3}{100}\)..

\(\frac{2}{m}=\frac{7}{100}\)..

We are looking for \(\frac{2}{m}+\frac{1}{b}=7/100+1/100=8/100\)..

So time taken=100/8=12.5..

thank you for reply..I have been preparing for gmat since few months.For quant, i am doing manhattan,

and some gmat club solution mainly you , Bunnel after completing official sources.. I think this problem is consistent with gmat quant that's why i have posted.