rohan2345 wrote:
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
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!)
\(\boxed{10\,\,mach}\,\,\,\,\, \to \,\,\,\,\frac{{40\,\,{\text{cans}}}}{{8\,\,{\text{s}}}} = \boxed{\frac{{5\,\,{\text{cans}}}}{{1\,\,{\text{s}}}}\,\,\,\begin{array}{*{20}{c}}
\nearrow \\
\nearrow
\end{array}}\)
\(12\,\,mach\,\,,\,\,\,600\,\,cans\,\,\,\,\, \to \,\,\,\,?\,\,\,:\,\,\,{\text{time}}\,\)
\(12\,\,mach\,\,\,\, = \,\,\,\boxed{10\,\,mach}\,\,\left( {\frac{{12}}{{10}}} \right)\,\,\,\, \to \,\,\,\,\,\boxed{\frac{{5\,\,{\text{cans}}}}{{1\,\,{\text{s}}}}}\,\,\,\frac{{12}}{{10}}\,\,\,\,\,\, \to \,\,\,\,\,\frac{{6\,\,\,{\text{cans}}}}{{1\,\,\,{\text{s}}}}\)
\(? = 600\,\,{\text{cans}}\,\,\,\left( {\frac{{1\,\,s}}{{6\,\,{\text{cans}}}}\,\,\begin{array}{*{20}{c}}
\nearrow \\
\nearrow
\end{array}} \right)\,\,\, = \,\,\,100\,\,{\text{s}}\)
Obs.: arrows indicate
licit converters.
The above follows the notations and rationale taught in the GMATH method.
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GMATH method creator (Math for the GMAT)
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