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Twelve identical machines, running continuously at the same [#permalink]
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31 May 2010, 14:30
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Twelve identical machines, running continuously at the same constant rate, take 8 days to complete a shipment. How many additional machines, each running at the same constant rate, would be needed to reduce the time required to complete a shipment by two days? A. 2 B. 3 C. 4 D. 6 E. 9
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Last edited by Bunuel on 29 Sep 2013, 08:57, edited 2 times in total.
Renamed the topic, edited the question and added the OA.



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Re: Rate & Work [#permalink]
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31 May 2010, 15:55
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One way is to think "faster by what ratio?" or "the same job in what fraction of the time?"We want to reduce the time by 2 days from the original 8 days: 6 days to complete. 6 days is 3/4 of the original 8 days. Since R = W/T, if R is constant, T of 3/4 as much implies W of 4/3 as much. In other words, if each machine doesn't speed up individually, you have to have 4/3 as many machines doing the work. 4/3 of the original number of machines (12) is 16 machines, or 4 additional machines. Another way is to pick some smart numbers to make the problem more "real." We have 12 machines working 8 days to make complete one "shipment." Let's say the shipment is 96 widgets (that's just 12*8). So the 12 machines make 12 widgets a day, which means each machine makes 1 widget a day (easiest number to work with!). To complete the 96 widgets in 6 days, then, you'd need 16 widgets each day, or 16 machines working. 4 additional machines.
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Re: Rate & Work [#permalink]
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31 May 2010, 18:36
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Another approach:
consider 12 machines to be 1 man (suppose).
Now the question is if 1 man can complete a task in 8 days how many men are needed to complete the same task in 6 days.
Simple unitary method:
To complete the work in 8 days  1 man is needed To complete the work in 1 day  (1X8) men needed To complete the work in 6 days  (1x8)/6
Which means that if I want to complete the same work in 6 days I would need 4/3 times initial effort i.e. if I had 12 machines initially I would now need (4/3)x12=16
Thus 4 more machines needed
OA C



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Re: Rate & Work [#permalink]
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05 Jun 2010, 01:33
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12machines8 days 1 shipment 1machine 96 days 1 shipment x machines 6 days 1 shipment
work rate*time
96=6x
x=16 4 more machines needed from original number of machines



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Re: Rate & Work [#permalink]
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05 Jun 2010, 08:57
we know that w = R*T work is constant here in both the cases. so R = 1/T 12 > 1/8 x > 1/6 12/x = 6/8 x= 16 (so 1612 = 4 more machines will be required.)



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Re: Rate & Work [#permalink]
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05 Jun 2010, 14:11
Thanks. Your help is much appreciated.



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Re: Rate & Work [#permalink]
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28 Sep 2013, 10:21
Rate(12) = 1/8 Rate(1) = 1/96 Rate * Time = Work 1/96 * Time = 1 1/96 * 6 = 1 What number of machines must be multiplied by 1/96 to make it 1/6 16, and knowing that we used 12 machined already the additional machine number is 4. Hence (C)
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Re: Twelve identical machines, running continuously at the same [#permalink]
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Rate = job / time
12 machines do 1 job in 8 days: 12x = 1/8 ==> x = 1/96 Rate of one machine = 1/96
Job reduced by 2 days means the job needs to be completed in 6 days. How many machines can do the job in 6 days? ==> 1/96*x = 1/6 ==> x = 96/6 ==> x = 16
Additional machines: 1612 = 4 machines
Answer: C



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Re: Twelve identical machines, running continuously at the same [#permalink]
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Re: Twelve identical machines, running continuously at the same [#permalink]
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Another way to look at it... Assume each machine completes 1 unit of work a day. 12 machines complete 12 units of work a day. in 8 days number of units completed is 12*8 = 96 units. Now number of machines required to complete 96 units in 6 days is 96/6 = 16. Additional number of machines required will be 1612 = 4.
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Re: Twelve identical machines, running continuously at the same [#permalink]
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11 Jan 2015, 06:35
12 machines * 8 days = 96 work days N machines * 6 days = 96 work days N = 96/6 = 16 i.e. 4 more machines Answer: C



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Twelve identical machines, running continuously at the same [#permalink]
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01 Mar 2015, 00:29
Since rate is constant, therefore 12 machines * 8 days = (x + 12)machines * 6days x= additional machine required 6days(8days 2days)=Number of days left after reducing by 2 days 96 = 6x + 72 x = 4 , OPTION C
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Re: Twelve identical machines, running continuously at the same [#permalink]
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13 Mar 2016, 01:42
12*8=6*x 96=6x x=16 1612=4 Additional Machines required



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Re: Twelve identical machines, running continuously at the same [#permalink]
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13 Mar 2016, 03:51
gsaxena26 wrote: Twelve identical machines, running continuously at the same constant rate, take 8 days to complete a shipment. How many additional machines, each running at the same constant rate, would be needed to reduce the time required to complete a shipment by two days?
A. 2 B. 3 C. 4 D. 6 E. 9 12 machines take 8 days to complete the task. We need to find the number of machines to complete the same task in 6 days. Machines and time are in inverse proportion. To increase the number of machines multiply with increasing ratio' 12*8/6 = 16 machines Therefore, 4 additional machines are required.



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Re: Twelve identical machines, running continuously at the same [#permalink]
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03 Apr 2016, 00:27
Use formula M1xD1/w1=M2xD2/W2
W1=W2=1 M1=12 D1=8 M2=? D2=82=6 put above values in the formula ans is 16. Machine already in use 12 difference =4 additional machines are required.
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Re: Twelve identical machines, running continuously at the same [#permalink]
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03 Apr 2016, 04:36
gsaxena26 wrote: Twelve identical machines, running continuously at the same constant rate, take 8 days to complete a shipment. 12 *r*8 = 96r gsaxena26 wrote: How many additional machines, each running at the same constant rate, would be needed to reduce the time required to complete a shipment by two days? (12+m)*r*6 = 96r 12+m = 16 m = 4 So, We require 4 additional workers.
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Re: Twelve identical machines, running continuously at the same [#permalink]
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29 Aug 2016, 12:31
I think I have an easier way... From the question you know that 12R = 1/8. The question asks you (partially) to make the rate from 1/8 to 1/6 (drop from 8 day to 6). So the only thing that you need to do is to find the magic number than can convert 1/8 to 1/6. So 1/8 * x = 1/6 (1 equation with one unknown). So by solving this you get x = 8/6 or 4/3. Thats it then! Take the magic number 4/3 and multiply BOTH sides of the original equation and you have: 12*(4/3)*R = (4/3) * 1/8 4 * 4 * R = 1/6, Hence 16R = 1/6, therefore 4 more machines!



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Re: Twelve identical machines, running continuously at the same [#permalink]
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29 Aug 2016, 14:02
let m=total machines needed rate of 1 machine=1/96 m*1/96*6=1 m=16 1612=4 additional machines needed



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Re: Twelve identical machines, running continuously at the same [#permalink]
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29 Aug 2016, 19:08
gsaxena26 wrote: Twelve identical machines, running continuously at the same constant rate, take 8 days to complete a shipment. How many additional machines, each running at the same constant rate, would be needed to reduce the time required to complete a shipment by two days?
A. 2 B. 3 C. 4 D. 6 E. 9 12 M 8 D 96 MD 96/6 = 16 Machines ie 4 additional MAchines are required
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Re: Twelve identical machines, running continuously at the same [#permalink]
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17 Sep 2016, 22:28
Since 12 machines take 8 days to complete the task, then in terms of rate 12 (1/X) = 1/8 [1/X is the rate of machine & 1/8 is the work completed by the 12 machines at rate of 1/X].
Solving for X, X=96. If 12 machines take 8 days to complete 96 units of work. Then I would need 4 additional machines to complete the work before 2 days.




Re: Twelve identical machines, running continuously at the same
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