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x identical machines can make x widgets in x minutes. If each machine

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x identical machines can make x widgets in x minutes. If each machine [#permalink]

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x identical machines can make x widgets in x minutes. If each machine works at the same constant rate, how many widgets can y identical machines make in y minutes, in terms of x and y?

A. x
B. y
C. y^2
D. x/y
E. y^2/x
[Reveal] Spoiler: OA

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x identical machines can make x widgets in x minutes. If each machine [#permalink]

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x machine-------x minutes---------x widgets

x machine-------1 minutes---------x /x widgets(=1 widget)

1 machine-------1 minutes---------1/x widgets (rate of x machine)

similarly
let Y machine in y minutes make A widget. then

y machine-------y minutes---------A widgets

y machine-------1 minutes---------A/y widgets

1 machine-------1 minutes---------A/y^2 widgets (rate of y machine)

As rates are equal

A/y^2 = 1/x
A =y^2/x

Ans E
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x identical machines can make x widgets in x minutes. If each machine [#permalink]

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New post 24 Apr 2017, 10:57
Number of Widgets is directly proportional to Number of machines and Time taken.

So we can write it as \(W ∝T*N\) ==> \(W=K*T*N\)

Where
W= Number of Widgets
T= Time Taken
N= Number of Machine
K= Equation constant (Don't Worry about this :wink:)

From the given Problem

\(x=K*x*x\)

On Solving above equation \(K=\frac{1}{x}\)

\(Wy= K*y*y\)

on substituting \(K=\frac{1}{x}\) ==> \(Wy=\frac{y^2}{x}\)


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Re: x identical machines can make x widgets in x minutes. If each machine [#permalink]

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New post 27 Apr 2017, 16:11
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Bunuel wrote:
x identical machines can make x widgets in x minutes. If each machine works at the same constant rate, how many widgets can y identical machines make in y minutes, in terms of x and y?

A. x
B. y
C. y^2
D. x/y
E. y^2/x


We are given that x identical machines can make x widgets in x minutes. Thus, the rate for the x machines is x/x or 1 widget per minute. Next we can determine the rate of y machines using the following proportion in which n is the rate for y machines:

x/1 = y/n

n = y/x

Since the rate for y machines is y/x and work = rate x time, y machines can produce (y/x)(y) = y^2/x widgets in y minutes.

Answer: E
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Re: x identical machines can make x widgets in x minutes. If each machine [#permalink]

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New post 02 May 2017, 14:29
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x identical machines.......working x minutes......can make= x widgets

1 identical machines.......working 1 minutes......can make[less] = x/(x+x) widgets

y identical machines.......working y minutes......can make[more] = (x/(x+x))*(y*y) widgets
= y^2 /x widgets

Answer: E
Re: x identical machines can make x widgets in x minutes. If each machine   [#permalink] 02 May 2017, 14:29
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