It takes 10 type A machines 3 days to complete a task when they are op

Question

It takes 10 type A machines 3 days to complete a task when they are operated 12 hours a day. How long will it take 8 Type B machines to complete the same task when they are operated 8 hours a day?

(1) Type B machines are 20% less efficient than Type A machines
(2) Type B machines take 25% longer to complete the same task than Type A machines

GMATinsight · Accepted Answer

GB11992  Your calculation is incorrect because we don't know (without statement) the relationship between the efficiencies of A and B and it will be wrong to assume that A is as efficient as B (Assumptions are fatal)

The video solution explains the steps

Answer: Option D

https://www.youtube.com/watch?v=nso_kQPBhWc

LeoN88 · Answer

Now 10.a.3.12 = Total Work (W) given, we have to find x
Where 8.b.x.8 = W

(1) b= .8*a. sufficient to find x
(2) b*125 = a*100, sufficient to find x.
 D

GB11992 · Answer

Bunuel  - Could you please explain how does machine rate factor in here? And also explain both the statements.
 
We can find the same using 10*3*12=8*D*8, since work is constant. Using which the answer would be D=5.625 days

Sorry for the mistake as this is the first time I'm writing a comment/quote on a question.

Target4bschool · Answer

What does efficiency means here? Any relevant formula to find the efficiency?

Tonkotsu · Answer

From what I see here, efficiency is the same exact thing as  \frac{work}{hour} .
Meaning that if machine A's efficiency is 20% greater than that of B, we can show that the work rate is:

(0.8)\frac{Work_A}{Hours_A} = \frac{Work_B}{Hours_B}

or

(1-\frac{20}{100})A = B

CEdward · Answer

VeritasKarishma  Can you explain which formula we should be using here? How does the number of days and hours come into play?

KarishmaB · Answer

CEdward You can use the same formula Work = Rate * Time or the concept of variation here. Say rate of each machine A is R. Then rate of 10 machines will be 10R. Time taken to complete work = 3*12 = 36 hours So work = 10R*36 = 360R (1) Type B machines are 20% less efficient than Type A machines If B machines are 20% less efficient, it means their rate of work is (4/5)R "How long will it take 8 Type B machines to complete the same task when they are operated 8 hours a day?" Work = Rate*Time 360R = (4/5)R*8 * Time Time = 225/4 hrs Sufficient alone. (2) Type B machines take 25% longer to complete the same task than Type A machines Time taken by machine B is 25% more means rate of machine B is 4/5th. Same analysis as statement 1. Sufficient alone. Answer (D) Suggest you to check out these posts: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/0 ... -problems/ https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2013/0 ... variation/

Hoozan · Answer

GMATinsight  instead of solving statement (2) as shown in your video could we simply do 1.25 * 8 * 3 and get our answer? Because we are already given the total time of A and we know the relationship of time B with time A, thereby we can find the time taken for B

CrackverbalGMAT · Answer

It takes 10 type A machines 3 days to complete a task when they are operated 12 hours a day. How long will it take 8 Type B machines to complete the same task when they are operated 8 hours a day?

Let's assume that per hour work rate of machine A be a and machine B be b.
 No of the days taken by machine B to complete the same task be x.

Since the amount of work completed in same in both cases, we can equate as

10 * a * 3 * 12 = 8 * b * x *8.

If we know the relation between a and b, we can find the value of x.

(1) Type B machines are 20% less efficient than Type A machines

From st.1 we can conclude that b= 80%of a i.e b=.8a
Sufficient to find the value of x.

(2) Type B machines take 25% longer to complete the same task than Type A machines

Time taken by machine B is 125% of time taken by machine A to complete the same task.
i.e Time taken by machine B = 5/4 * Time taken by A

So we can infer that Per hour work rate of B = 4/5 *Per hour work rate of A
 i.e b = 4/5 a

Sufficient to find the value of x.

Option D is the answer.

Thanks,
  Clifin J Francis

Tishaagarwal13 · Answer

10 Type A - 3 days - 12 hours

So, total time = 3*12 = 36 hours
Let the work be 1

We can say that rate of 10 machines = 1/36

8 Type B - x days - 8 hours

Statement 1: Type B machines are 20% less efficient than Type A machines - This means Type B machines will take more time to complete the work than Type A machines. We can calculate the new rate and hence the time - Sufficient

Statement 2: Type B machines take 25% longer to complete the same task than Type A machines - We know that 10 Type A machines took 36 hours to complete the work. So, type B machines will take 25% longer - Sufficient

The  correct answer is D

It takes 10 type A machines 3 days to complete a task when they are op

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It takes 10 type A machines 3 days to complete a task when they are op

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