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.

_________________

Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or GMATH.com.br (Portuguese version)

Course release PROMO : finish our test drive till 30/Nov with (at least) 50 correct answers out of 92 (12-questions Mock included) to gain a 50% discount!