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# A certain manufacturer has three machines producing the same item. If

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Math Expert
Joined: 02 Sep 2009
Posts: 50009
A certain manufacturer has three machines producing the same item. If  [#permalink]

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04 Feb 2018, 21:40
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Difficulty:

15% (low)

Question Stats:

92% (01:27) correct 8% (01:43) wrong based on 35 sessions

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A certain manufacturer has three machines producing the same item. If Machine X produces 1/4 as many of the item as Machine Y produces in the same time, and Machine Y produces twice as many of the item as Machine Z in the same time, then during a fixed period Machine Z produces what fraction of the total number of items produced?

(A) 1/14
(B) 2/7
(C) 1/3
(D) 1/2
(E) 4/7

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Concentration: Operations, Strategy
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Re: A certain manufacturer has three machines producing the same item. If  [#permalink]

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04 Feb 2018, 21:48
B

Let the rate of machine X, Y and Z be x, y and z.

We have,

x=y/4

and

y=2z

So total productivity = x+y+z

=y/4+y+z

=2z/4+2z+z

=z/2+3z

=7z/2

Hence total number of items produced = time/rate

=2/7
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Intern
Joined: 04 May 2015
Posts: 17
Re: A certain manufacturer has three machines producing the same item. If  [#permalink]

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04 Feb 2018, 22:10
Bunuel wrote:
A certain manufacturer has three machines producing the same item. If Machine X produces 1/4 as many of the item as Machine Y produces in the same time, and Machine Y produces twice as many of the item as Machine Z in the same time, then during a fixed period Machine Z produces what fraction of the total number of items produced?

(A) 1/14
(B) 2/7
(C) 1/3
(D) 1/2
(E) 4/7

let the no. of items produced in time t by Y is a
so items produced by x be a/4
items produced by z be a/2
all items produced in time t=a/4+a+a/2=7a/4
fraction of work by z : (a/2)/(7a/4)=2/7
help with kudos if u liked my explaination.TIA
SVP
Joined: 26 Mar 2013
Posts: 1839
A certain manufacturer has three machines producing the same item. If  [#permalink]

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05 Feb 2018, 13:37
Bunuel wrote:
A certain manufacturer has three machines producing the same item. If Machine X produces 1/4 as many of the item as Machine Y produces in the same time, and Machine Y produces twice as many of the item as Machine Z in the same time, then during a fixed period Machine Z produces what fraction of the total number of items produced?

(A) 1/14
(B) 2/7
(C) 1/3
(D) 1/2
(E) 4/7

x : y
1: 4

y : z
2 : 1

To compare all ratios, we need to multiply y/z ration by 2......Hence

x : y : z
1: 4 : 2

$$\frac{Z}{total}$$ = $$\frac{2}{7}$$

A certain manufacturer has three machines producing the same item. If &nbs [#permalink] 05 Feb 2018, 13:37
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