1 man, 3 women, and 4 boys can do a piece of work in 96 hours; 2men an

Question

1 man, 3 women, and 4 boys can do a piece of work in 96 hours; 2men and 8 boys can do the same work in 80 hours, and 2 men and 3 women can do it in 120 hours. In how many hours can the same work be done by 5 men and 12 boys?

A. \(60\frac{3}{13}\) hours

B. \(40\) hours

C. \(43\frac{7}{11}\) hours

D. \(100\) hours

E. \(40\frac{7}{11}\) hours

A.  60\frac{3}{13}  hours

B.  40  hours

C.  43\frac{7}{11}  hours

D.  100  hours

E.  40\frac{7}{11}  hours

Are You Up For the Challenge: 700 Level Questions

Nidzo · Answer

(1)   \frac{1}{m}+\frac{3}{w}+\frac{4}{b} = \frac{1}{96}

(2)   \frac{2}{m}+\frac{8}{b} = \frac{1}{80}

(3)   \frac{2}{m}+\frac{3}{w} = \frac{1}{120}

Subtracting (1)  from  (2)  gives:  \frac{1}{m}+\frac{4}{b}-\frac{3}{w}=\frac{1}{480}

Add  (3)  to the above to get rid of the  w :  \frac{3}{m}+\frac{4}{b}=\frac{5}{480}

Add  (2)  to the above to have 5 men and 12 boys:  \frac{5}{m}+\frac{12}{b} = \frac{11}{480}

480÷11 = 43\frac{7}{11}  hours

Answer C

chetan2u · Answer

Another method. 
May seem long but is very quick if you grasp it.

The look at numbers should tell you to compare all of them.

1m+3w+4b can do the work in 96 hrs or 10 work 960 h but 2m+8b can do single work in 80h, meaning (2m+8b)/2 can do it in 2*80 or 160h. 
Thus 1m+4b can do 6 work on their own in 6*160 hrs, so 3w do 10-6 or 4 works in 960h or 1 work in 240h. 
 1 woman can do the work in 3*240 or 720h

Next 2m+3w can do one work in 120h or 2 work in 240h. But, 3w do one work in 240h, meaning the remaking work is done by 2m. 
 1 man can do the work in 2*240 or 480

Finally 1m and 4b can do a work in 160h or 3 work in 3*160 or 480h while 1m can do it in 480h. Thus 4b do the remaining 2 work in 480h. 
 1 boy can do the work in 480*4/2 or 960h

5m and 12 boys 
5m will do 5 work in 480h, while 12 boys can do 12 work in 960h or 6 work in 480h. 
Thus, 5m and 12b can do 5+6 or 11 work in 480h. 
Therefore, they can do one work in 480/11 hours.

C

NEO1902 · Answer

Could you please elaborate on how you're arriving at the values for 'work'...eg 96 hrs or 10 work.
Thanks.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

1 man, 3 women, and 4 boys can do a piece of work in 96 hours; 2men an

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

1 man, 3 women, and 4 boys can do a piece of work in 96 hours; 2men an

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards