10 factories, working for h hours per day, can produce P units of cars

Question

10 factories, working for h hours per day, can produce P units of cars in every 5 days. Each factory produces car at the same constant rate. What is the additional time taken by the 10 factories to produce 2P units of cars, if they work for h/2 hours per day instead of h hours per day?

A. 0
B. 2
C. 5
D. 10
E. 20

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A. 0
B. 2
C. 5
D. 10
E. 20

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aeforx · Answer

If the efficiency stay the same (they work h hours per day)
then 20 factories produce 2P units in 5 days (10 factories produce P in 5 days)
Now the factories work only h/2 per day, which means their efficiency is half of the one they used to have
hence they need to double the time to get 2P, 5*2=10, they need 10-5=5 additional days

dhart · Answer

Since for new setting , the production has to double and number of hours are halved , time taken can be 4 times the original time i.e 4 * 5 is 20 option e)

krtkshrvstv · Answer

It is not saying another 10 factories, it is asking how much will those same 10 factories take

onlyPlanA · Answer

That's right. It's asking how much more time those  same 10 factories  will take to produce 2P cars.

krtkshrvstv , Welcome to the gmat club!

abhishekb1352 · Answer

Let me give this question a try, I will be using the manhours concept here.

Work done = no of units produced = Rate * Time, let R be the rate of each factory.
P = 10*5*h*R --> R = P/50h

Now let us calculate how much time it would take for the same factory working at h hours per day to produce 2P units.
2P = 10*h*P/50h*T1
T1 = 10 days

Now we need to calculate how much time it would take for the same 10 factories working at h/2 hrs per day to produce the 2P units 
2P = 10*h/2*P/50h*T2
T2 = 20 days.

Additional number of days to produce 2P units working at h/2 hrs per day would be T2 - T1 = 10 days (Option D)

chetan2u · Answer

Things to remember...
 Addl  time and  2P  units..

First case...10 factories will make 2P units in double the time, so 5*2 or 10 days.

Second case...If time is halved, then 10 factories will take 10*2 or 20 days.

Addl time = 20-10 or 10 days..

D

SolarNote · Answer

I belive there is a slight bit of confusion here, would be great if someone lets me know the tell to recognise why we had to check for 2P units even in the first case. The question has only set 2 conditions.

Condition 1 :-
P cars produced by 10 factories in 5 days working for h hrs.

Condition 2 :-
2P cars produced by same 10 factories in x days working for h/2 hrs.

So should we not have to find x (condition 2) - 5 (condition 1)and our answer should be 15?

chetan2u · Answer

What is the additional time taken by the 10 factories to produce 2P units of cars, if they work for h/2 hours per day instead of h hours per day?

The above clearly speaks of the effect of change in hours per day on manufacturing 2P units of cars.

Maybe the language in the case suggested by you would be  
  What will be the additional time taken by the 10 factories if they were to produce 2P units of cars working for h/2 hours per day instead of h hours per day?  
 What will be the additional time taken by the 10 factories if they were to produce 2P units of cars ?

dhart · Answer

the question has a typo

10 factories, working for h hours per day, can produce P units of cars

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10 factories, working for h hours per day, can produce P units of cars

Prep Toolkit

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

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