If all machines in a factory are equally efficient and 10 machines

Question

If all machines in a factory are equally efficient and 10 machines take 8 seconds to produce 40 cans, how long will it take 12 machines to produce 600 cans?

A- 25 seconds
B- 50 seconds
C- 1 minute and 40 seconds
D- 2 minutes
E- 3 minutes and 20 seconds

ScottTargetTestPrep · Accepted Answer

Since the rate of 10 machines is 40/8 = 5, the rate for 1 machine is 5/10 = 1/2 and the rate for 12 machines is 1/2 x 12 = 6.

Thus, it takes 12 machines 600/6 = 100 seconds = 1 minute 40 seconds to produce 600 cans.

Answer: C

CounterSniper · Answer

\frac{M1*D1*H1}{W1}  =  \frac{M2*D2*H2}{W2}

substituting the values

\frac{10*8}{40} =  \frac{12*t}{600} 
t=100 seconds=1 minute 40 seconds

fskilnik · Answer

Excellent opportunity to use UNITS CONTROL, one of our most powerful tools!

(The solution may seem excessively "sophisticated", but it works in much hard/high-level question scenarios!)

\boxed{10\,\,mach}\,\,\,\,\, 	o \,\,\,\,\frac{{40\,\,{	ext{cans}}}}{{8\,\,{	ext{s}}}} = \boxed{\frac{{5\,\,{	ext{cans}}}}{{1\,\,{	ext{s}}}}\,\,\,\begin{array}{*{20}{c}}
 
earrow \ 
 
earrow 
\end{array}}

12\,\,mach\,\,,\,\,\,600\,\,cans\,\,\,\,\, 	o \,\,\,\,?\,\,\,:\,\,\,{	ext{time}}\,

12\,\,mach\,\,\,\, = \,\,\,\boxed{10\,\,mach}\,\,\left( {\frac{{12}}{{10}}} ight)\,\,\,\, 	o \,\,\,\,\,\boxed{\frac{{5\,\,{	ext{cans}}}}{{1\,\,{	ext{s}}}}}\,\,\,\frac{{12}}{{10}}\,\,\,\,\,\, 	o \,\,\,\,\,\frac{{6\,\,\,{	ext{cans}}}}{{1\,\,\,{	ext{s}}}}

? = 600\,\,{	ext{cans}}\,\,\,\left( {\frac{{1\,\,s}}{{6\,\,{	ext{cans}}}}\,\,\begin{array}{*{20}{c}}
 
earrow \ 
 
earrow 
\end{array}} ight)\,\,\, = \,\,\,100\,\,{	ext{s}}

Obs.: arrows indicate  licit converters .

The above follows the notations and rationale taught in the GMATH method.

BrentGMATPrepNow · Answer

We can also use some  number sense  to get to the correct answer...

GIVEN:  10  machines take   8   seconds to produce  40  cans
So,  10  machines take   1   second to produce  5  cans  (if we divide the work time by 8, then the output is also divided by 8) 
So,  1  machines take   1   second to produce  0.5  cans  (if we divide the number of machines by 10, then the output is also divided by 10) 
So,  12  machines take   1   second to produce  6  cans  (if we multiply the number of machines by 12, then the output is also multiplied by 12)

We now know that  12  machines take   1   second to produce  6  cans 
We want the 12 machines to make 600 cans. 
600/ 6  = 100
So,  12  machines take   100   seconds to produce  600  cans

100 seconds = 1 minute and 40 seconds.

Answer: C

EgmatQuantExpert · Answer

Solution

Given  
 • All machines of a factory are equally efficient.
• 10 machines take 8 seconds to produce 40 cans.

To find  
 • Time taken by 12 machines to fill 600 cans.

Approach and Working out

10 Machines take 8 seconds to fill 40 cans.
 • So, each machine is working 8 seconds. And total 80 seconds.
 o So, if 1 machine had been working then it would take 80 seconds to fill 40 cans.
  80 seconds to fill 40 cans.
 So, 1 machine will take 2 seconds to fill 1 can. 
• So, 12 machines in 2 seconds can fill 12 cans.
o 12 cans -> 2 seconds 
o 12 * 50 cans = 600 cans -> 2 * 50 =100 seconds= 1 min 40 sec

Thus, option C is the correct answer.

Correct Answer: Option C

raghav1708 · Answer

Your explanations are always perfect. Thank you for the help that you have given Scott!  ScottTargetTestPrep 
Gratitude

ScottTargetTestPrep · Answer

Sure thing!

Paras96 · Answer

If all machines in a factory are equally efficient and 10 machines take 8 seconds to produce 40 cans, how long will it take 12 machines to produce 600 cans?
SOLUTION:- (M1D1H1/W1)= (M2D2H2/W2)
 (10*8)/40=(12*x)/600 
 where x is the time taken to produce 600 cans
 x = 100 seconds or 1 minute 40 seconds
   Hence C

Gemmie · Answer

10m --- 8s --- 40c
2m 40s 40c
12m 40s 240c
12m 20s 120c
12m 100s 600c

=> 100s = 60s + 40s = 1m40s

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.

If all machines in a factory are equally efficient and 10 machines

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

If all machines in a factory are equally efficient and 10 machines

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