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Director
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Machine A and Machine B are each used to manufacture 660 [#permalink]
 18 May 2006, 19:34
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Machine A and Machine B are each used to manufacture 660 sprockets. It takes machine A 10 hours longer to produce 660 sprockets than machine B. Machine B produces 10% more sprockets per hour than machine A. How many sprockets per hour does machine A produce
A. 6
B. 6.6
C. 60
D. 100
E. 110
This took me a long time to calculate and figure out. Does anyone have a quick method that you can show me?
Source suggested backsolving due to time constraints.
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Manager
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Using POE, answers C, D and E look too big because the difference in time it takes for A and B is [u]only[/u] 10% and it takes [u]10 hrs more [/u] for A than B to make 660.
Now going by backsolving, start with A (as it's easy one without decimals :-D ).
If A makes 6/hr --> B makes 6.6/hr.
It takes A 110 hrs for 660 sprockets (ot whatever they are) and
it takes B 100 hrs for the same.
Hence A.
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Manager
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B = x hrs to produce 660
A = x + 10 hrs to produce 660
in one hr B produces 660/x
in one hr a produces 660/x + 10
660/x - 660/x+10 = 1/10(660/x+10)
solving we get x = 100
x + 10 = 110...
Thus Aproduces 660/110 =6 sprockets in an hour.
I couldnt think of a faster approach, but the above one dint take much time either.
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GMAT Club Legend
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Machine B: Takes x hours to produce 660 sprockets
Machine A: Takes (x+10) hours to produce 660 sprockets
Machine B: In 1 hour, B makes 660/x sprockets
Machine A: In 1 hour, A makes 660/(x+10) sprockets
Equating:
1.1(660/(x+10)) = 660/x
726/(x+10) = 660/x
726x = 660x+6600
66x = 6600
x = 100
A makes 660/(110) = 6 sprockets per hour
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Director
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We get two equations here for number of sockets by B in 1hr
Let time taken by A for 660 sockets = x
1) B in 1 hr = 1.1 * (a in 1 hr)
ie. 1.1 * 660/x = 726/x
2) B taken 10 hrs less than A for 660 sockets
660 sockets in (x-10) hrs
Therefore 1hr = 660/x-10
Using these two,
726/x = 660/(x-10)
So, x = 110.
In 1 hr A makes 660/110 = 6 sockts
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