Machines M and N produce identical widgets but at different constant r

Question

Machines M and N produce identical widgets but at different constant rates. Machine M takes 10 hours to produce 1000 widgets and Machines M and N together take 6 hours and 40 minutes to produce 2000 widgets. How much time does Machine N take to produce 3000 widgets?

A. 3 hours
B. 5 hours
C. 9 hours
D. 10 hours
E. 15 hours

A. 3 hours
B. 5 hours
C. 9 hours
D. 10 hours
E. 15 hours

karnavora1 · Answer

Pretty straight forward question

Machine M makes 1000 widgets in 10 hours or 600 minutes.
It will take Machine M 1200 minutes to make 2000 widgets

Together Machine M and N take 400 minutes to make 2000 widgets.

Let's consider 2000 widgets as 1 work

1/M + 1/N = 1/400
1/1200 + 1/N = 1/400
1/N = 600

N takes 10 hours to make 2000 widgets
Hence N will take 15 hours to make 3000 widgets

Answer is E.

Please give me Kudos if this helps.

yashikaaggarwal · Answer

It tools A to make 1000 widgets in 10 hours.
1000 widgets in 10*60=600 min
1.666 widgets in a min

A and B together make 2000 widgets in 400 minutes (6hours40min)
A can make 1.66*400 widgets in 400 min
A can make 666.66 widgets in 400 min.
B made 2000-666.66 widgets 1333.34 in 400 min
B can make 3.333 in a min
B can make 3000 in Y min
Y = 3000/3.333 = 900 min.
900 min / 60 = 15 hours. 
Answer is E

Posted from my mobile device

satya2029 · Answer

(M+N)*20/3=2000
M+N=300
AS M= 1000/10=100
N=200
in 1 Hr N produce 200 widgets 
Time= (3000*1)/200
T=15
E:)

suchita2409 · Answer

Combined time can be given by
(A*B)/(A+B)
where a and b are the respective times taken by the machines.
We know from the stem that it takes 20 hrs for producing 2000 widgets.

(20x)/(20+x) = 20/3 hrs.

the value of x is 10 .i.e. the time required by machine N to produce 2000 widgets.

for 3000 widgets it takes 15 hrs.

E.

Posted from my mobile device

GMATinsight · Answer

M's 1 hours work = 1000/10 = 100 widgets

M+N's 1 hours work = 2000/(20/3) = 300 widgets  (6 hours 40 minutes = 6 2/3 hours = 20/3 hours0

i.e. N's 1 hour work = 300-100 = 200 widgets

Time of N to make 3000 widgets = 3000/200 = 15

Answer: Option E

Archit3110 · Answer

rate of M = 1000/10 ; 100 widgets per hour
and total time of M +N to make 2000 widgets ; 6hrs+40/60 ; 20/3 hrs
find combined rate of M+N to make 2000 widgets ; 2000/20 *3 ; 300 widgets per hour
we know M +N = 300 and M =100 so N =200
so to make 3000 widgets N take ; 3000/200 ; 15 hours
OPTION E

SidhantGupta04 · Answer

M's rate is 10/6 widget/minute  
M and N combined rate is 5 widget/minute

N's rate = 5- 10/6 = 20/6 widget/minute

Time taken by N for 3000 widgets= 3000*6/20 = 900 minutes= 15 hours

Machines M and N produce identical widgets but at different constant r

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Machines M and N produce identical widgets but at different constant r

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards