Machine X can produce 3 widgets every 2 minutes and Machine Y produces

Question

Machine X can produce 3 widgets every 2 minutes and Machine Y produces 5 widgets every 3 minutes. If both the machines work together for 25 minutes what part of the production will be finished by Machine X?

(A) 2/19
(B) 3/19
(C) 4/19
(D) 5/19
(E) 9/19

(A) 2/19
(B) 3/19
(C) 4/19
(D) 5/19
(E) 9/19

chetan2u · Accepted Answer

Machine X ..
3 widgets in 2 minutes, so 3/2 widget in 1 minute....
Therefore 25*3/2=75/2 in 25 minutes

Machine Y
5 widgets in 3 minutes, so 5/3 widget in 1 minute....
Therefore 25*5/3=125/3 in 25 minutes

Total widgets = (75/2+125/3)=(225+250)/6=475/6
Machine X's work = (75/2)/(475/6)=(75*6)/2*475 = (25*3*6)/(25*19*2)=9/19

E

Archit3110 · Answer

Machine X can produce 3 widgets every 2 minutes and Machine Y produces 5 widgets every 3 minutes. If both the machines work together for 25 minutes what part of the production will be finished by Machine X?

(A) 2/19
(B) 3/19
(C) 4/19
(D) 5/19
(E) 9/19

(A) 2/19
(B) 3/19
(C) 4/19
(D) 5/19
(E) 9/19

Work per minute of x : 3/2 and y : 5/3

Combined rate shall be {(3/2)+(5/3)}: 19/6
in 25 mins work would be (19/6)*25

X work in 25 mins (25 * x rate); 25* (3/2)

Part of work done by X in 25mins for combined work done :

[ (6/19)*(1/25) * (3/2)* 25)
=> 9/19

Abhishek009 · Answer

Efficiency of Machine X = 3/2 widgets per minute
Efficiency of Machine Y = 5/3 widgets per minute

So, In 6 Minutes X Produces 3/2*6 = 9 widgets
And In 6 Minutes X Produces 5/3*6 = 10 widgets

Thus, in 6 minutes Machine X and Y produces 19 widgets and X's contribution is 9/19 widgets, Answer must be (E)

generis · Answer

One approach: find (Part X : Part Y)
Then (Part X : Whole X+Y)

I.  Change the time, find (part: part) ratio, then (part: whole)    
Use ANY easier time period to find PART : PART ratio

Relative portions that X and Y finish  will not change  as long as time worked is the same
 X 's part of total production is:   \frac{X}{X+Y}

(1)  Change the time period. 
• X's output + Y's output = total output

• Total output for each is:

X :  r_{x}*T=W_{x}

Y :  r_{y}*T=W_{y}

Same time worked? Then number of widgets each makes depends ONLY on their rates.

(2) : compare  rates  with a time that is easier than 25 minutes 
• Use LCM of 6 minutes to get an identical time period worked, which will yield
relative portions of total work each produces

X 's rate in 6 minutes:  \frac{3w}{2min}=\frac{9w}{6min}

Y 's rate in 6 minutes:  \frac{5w}{3min}=\frac{10w}{6min}

• The part of production finished by X?

\frac{X}{(X+Y)}=\frac{9}{9+10}=\frac{9}{19}

Answer E

II. Harder: TOTAL output in 25 minutes  
In 25 minutes, X finishes   \frac{X_{w}}{Total_{w}}

•  X , total output:

W_{x}=r_{x}*25

W_{x}=(\frac{3w}{2min}*25min)=\frac{75}{2}w

•  Y , total output

W_{y}=r_{y}*25

W_{y}=(\frac{5w}{3min}*25min)=\frac{125}{3}w

• Overall total output (X + Y):

(X+Y)=(\frac{75}{2}w+\frac{125}{3}w)=

(\frac{225}{6w}+\frac{250w}{6}w)=\frac{475}{6}w

• X finishes what part of total production?

\frac{X}{Total}=\frac{(\frac{75}{2}w)}{(\frac{475}{6}w)}=

(\frac{75}{2}w*\frac{6}{475}w)=    \frac{225w}{475w} 
 
Divide by 25:

X finishes  \frac{9}{19}  of production

Answer E

ScottTargetTestPrep · Answer

Machine X’s rate is 3/2, and Machine Y’s rate is 5/3. Their combined rate is (3/2 + 5/3). We can create the expression:

(3/2)/(3/2 + 5/3)

Multiplying the expression by 6/6 we have:

9/(9 + 10) = 9/19

No matter the amount of time they work together, Machine X will always produce 9/19 of the combined output.

Answer: E

GMATGuruNY · Answer

For X, 3 widgets every 2 minutes = 9 widgets every 6 minutes.
For Y, 5 widgets every 3 minutes = 10 widgets every 6 minutes.
Thus, every 6 minutes:
Number of widgets produced by X = 9 
Number of widgets produced by Y = 10
Total number of widgets produced by X and Y together = 9+10 = 19

Since X produces 9 of every 19 widgets that are produced, we get:
 \frac{X}{total }= \frac{9}{19}

E

Felipe28g · Answer

While I got the answer right, I think this question is actually wrong. You can't have 41.66 and 37.5 widgets, and if the two machines are working separately you can't add those up. The number of widgets should be an integer and therefore the answer should be 9/10.

bumpbot · Answer

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Machine X can produce 3 widgets every 2 minutes and Machine Y produces

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