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2 men and 3 boys can do a piece of work in 10 days while 3 men and 2

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2 men and 3 boys can do a piece of work in 10 days while 3 men and 2  [#permalink]

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New post 16 Apr 2017, 06:20
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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
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Posts: 6265
Re: 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2  [#permalink]

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New post 16 Apr 2017, 09:53
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..
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Re: 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2  [#permalink]

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New post 16 Apr 2017, 12:45
Let x be men and y boys
(2y+3x)/xy=1/10
(3y+2x)/xy=1/8
Through elimination you will get
X=2/7y
Therefore 10/y=1/10
Y rate=1/100
X rate=3.5/100
So rate of 2x+y=8/100 or 1/12.5 per day. Therefore it will be completed in 12.5 day

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2 men and 3 boys can do a piece of work in 10 days while 3 men and 2  [#permalink]

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New post 16 Apr 2017, 14:10
1
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

let m and b=rates for 1 man and 1 boy respectively
multiplying,
6m+9b=3/10 and
6m+4b=1/4
subtracting,
b=1/100
m=3.5/100
let d=days
d(7/100+1/100)=1
d=12.5 days
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Re: 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2  [#permalink]

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New post 16 Apr 2017, 21:49
2
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


    • 2 men and 3 boys can do a piece of work in 10 days.
      o Thus, 20 men and 30 boys can do a piece of work in 1 day......(i)

    • 3 men and 2 boys can do the same work in 8 days.
      o Thus, 24 men and 16 boys can do the same work in 1 day....(ii)

    • Equating (i) and (ii) we get -
      o 20 men + 30 boys = 24 men + 16 boys
      o 4 men = 14 boys
      o 2 men = 7 boys

    • Substituting this in equation (i) we get

      o 10 boys can do a piece of work in 10 days.
      o But we need to find out in how many days 2 men and 1 boy can do the work, which is equivalent to 8 boys.

         8 boys can do the same work in (10*10/8) = 12.5 days.

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Re: 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2  [#permalink]

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New post 16 Apr 2017, 23:58
chetan2u wrote:
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, veritas 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. :-D
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Re: 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2  [#permalink]

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New post 19 Apr 2018, 09:48
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Re: 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 &nbs [#permalink] 19 Apr 2018, 09:48
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