Five machines at a certain factory operate at the same constant rate

Question

Five machines at a certain factory operate at the same constant rate. If four of these machines, operating simultaneously, take 30 hours to fill a certain production order, how many fewer hours does it take all five machines, operating simultaneously, to fill the same production order?

(A) 3
(B) 5
(C) 6
(D) 16
(E) 24

(A) 3
(B) 5
(C) 6
(D) 16
(E) 24

Kurtosis · Accepted Answer

Total work done by 4 machines = 30 * 4 = 120 units

When one more machine is added each machine works for --> 120/5 = 24 hours

Difference = 30 - 24 = 6hrs

Answer: C

chetan2u · Answer

4 machines do a work in 30 days..
1 machine will do that work in 30*4 days...
5 machines will do it in  30*\frac{4}{5}= 24.. 
lesser time =  30-24 = 6 
C

Abhishek009 · Answer

Total work = 4*30 machine hrs

Time taken = 4* 30 /5 => 24 hours...

Thus all five machines, operating simultaneously will take ( 30 - 24 ) 6 hours..
  
Answer will be (C) 6

Divyadisha · Answer

If 4 machines take 30 hrs, 5 machines will take 30*4/5= 24 hrs

How many fewer hours will all five machines take= 30-24= 6 hrs

C is the answer

nayanparikh · Answer

Let the rate of machine be x hours. So in hour it can complete 1/x of work. Four machine rate = 4*(1/x) = 4/x.
Now, Rate* Time = Job i.e. 4/x*30 = Job. So one machine can take 120 hour to complete the job.
Five machine works together it can take :120/5 = 24 hours to complete the job.
Hence 30-24 = 6 hours.

Answer is C.

adkikani · Answer

Hi  VeritasPrepKarishma   chetan2u   niks18   gmatbusters   Bunuel

Let me know if my below approach is correct using 'Joint variation'
as discussed  here

I have to find number of hrs when machines operating are increased from 4 to 5.
Simple logic says if I increase the no of machines, the no of hrs to complete the same work
will be reduced. Hence if I have initial no. of hrs defined, I need to multiply it by proper fraction
ie numerator/denominator < 1

Using above steps:
 
No of hrs = 30 (when 4 machines are operational)
I need to multiply this by 4/5 since I need a fraction less than 1. 
Hence I get 30 * (4/5) = 24 as hrs required when 5 machines are operational.

I already know that when 4 machines are working, I shall need 30 hrs. 
Hence, difference = 30-24 ie 6 hrs.

KarishmaB · Answer

Yes, absolutely correct.

ScottTargetTestPrep · Answer

The rate of 4 machines is 1/30.

We can let the rate of 5 machines be n and create the equation:

4/(1/30) = 5/n

120 = 5/n

120n = 5

n = 5/120 = 1/24

So it will take 1/(1/24) = 24 hours for the 5 machines to fill the same order and thus it takes 6 fewer hours than if the order were filled by 4 machines.

Answer: C

hasnain3047 · Answer

Rate if 4 machines 1/30
Rate of 1 machine = 1/(30*4)
Rate of 5 machines = 1*5/(30*4) = 1/24
So 5 machines complete work in 24 hourse and take 6 fewer hours.

Answer is C

Posted from my mobile device

Salsanousi · Answer

The question asks for the difference in hours

4 machines finish in 30 hours so 1 machine finishes in 120 hours.

5 machines will then finish in 120/5 = 24 hours.

The difference in hours is |24-30| = 6.

Answer choice C

kt9696 · Answer

4 machines take -> 30 hours
1 machine takes -> 30*4 hours
5 machines take -> 30*4/5 hours
Difference = 30*4/5-30= 6 hours

Answer (C) 6 hours

Basshead · Answer

We have 5 machines in a certain factory:

Four of these machines take 30 hours to fill a production order.

Therefore one machine takes 120 hours to fill a production order.

How many fewer hours does it take 5 machines to fill this order?

120 hours split by 5 machines = 24 hours per machine.

30 - 24 = 6 fewer hours.

Answer is C.

Anonymous · Answer

chetan2u  based on the rule of 3, isn't it as follows?

4 machines 30 hours
1 machine x hours

4*x = 30
x= 30/4

So, 5 machines need 5*x = 5*(30/4) = 150/4

Bunuel · Answer

It should be 4 * 30 = 5 * x, where x represents the number of hours needed for 5 machines to complete the task, giving x = 24. Thus, the difference is 30 - 24 = 6.

hkalabdu · Answer

**I assumed the constant rate is 1/2 and multiplied the # machines with assumed constant rate and given hours worked to arrive at production order

4 machines * 1/2 constant rate * 30 (#number of hours) = 60 (the production order)

5 Machines * 1/2 * x (#number of hours) = 60 ( same production order)

5x/2 = 60 >>>> x=120/5 = 24 hour.

Thus the 5 combines worked 6 hours less than than the four companies to produce the same production order

(30 hours - 24 hours) = 6

egmat · Answer

Here's how to think about this:

Step 1: Understand what we're comparing

You have 4 machines taking 30 hours to complete a job, and you need to find how many fewer hours it takes when all 5 machines work together. Notice the question asks for the  difference  in time, not just the time for 5 machines.

Step 2: Find the total work required

Here's the key insight: Let's think of the total work as "machine-hours." If 4 machines work for 30 hours, the total work is:

4 	imes 30 = 120  machine-hours

This tells you that no matter how you arrange the machines, the job always requires exactly 120 machine-hours to complete. This is your constant.

Step 3: Calculate time for 5 machines

Now that you know the total work is 120 machine-hours, you can find how long 5 machines take:

ext{Time} = \frac{	ext{Total work}}{	ext{Number of machines}} = \frac{120}{5} = 24  hours

Notice how this makes intuitive sense – more machines means less time!

Step 4: Find the difference

The question asks how many  fewer  hours with 5 machines:

30 - 24 = 6  hours

Answer: (C) 6

Why this approach works:  The key is recognizing that total work (machine-hours) stays constant. This transforms a potentially complex problem into simple arithmetic.

For the complete framework on work-rate problems, including how to spot variations of this question type and systematic approaches that work across all similar problems, you can check out the  detailed solution on Neuron by e-GMAT . You'll also find comprehensive explanations for  other official questions on Neuron  to build consistent accuracy on work-rate problems.

Hope this helps!

Five machines at a certain factory operate at the same constant rate

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Five machines at a certain factory operate at the same constant rate

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