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

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.

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

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

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

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

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/

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

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