M23-16

Question

When working together, printers A and B can finish printing the entire document in 24 minutes. If printer A by itself can finish printing the document in 60 minutes, how many pages does the document have if printer B prints 5 pages more per minute than printer A?

A. 600
B. 800
C. 1000
D. 1200
E. 1500

Show Answer

Official Answer

A

A. 600
B. 800
C. 1000
D. 1200
E. 1500

Bunuel · Accepted Answer

Official Solution:

When working together, printers A and B can finish printing the entire document in 24 minutes. If printer A by itself can finish printing the document in 60 minutes, how many pages does the document have if printer B prints 5 pages more per minute than printer A?

A. 600
B. 800
C. 1000
D. 1200
E. 1500

Show Answer

Official Answer

A

A. 600
B. 800
C. 1000
D. 1200
E. 1500

Let  a  denote the number of pages Printer A prints in one minute.
 
Let  b  denote the number of pages Printer B prints in one minute.
 
Given that printers A and B together can print the entire document in 24 minutes, the total number of pages in the document is  24a + 24b .
 
However, when Printer A works alone, it completes the document in 60 minutes, implying the document consists of  60a  pages.
 
Thus,  24a + 24b = 60a . Given that  b = a + 5 , we would get  24a + 24(a + 5) = 60a , which results in  a=10 .
 
Therefore, the document has  60a=600  pages.

Answer: A

chetan2u · Answer

hi,
I am not sure if it can be done by weighted average, as it is more to do with allegations and mixture and the averages..
It is not the case here..

I'll just tell you two methods here..

1) both finish the work in 24 minutes..
 so A does 24/60=2/5 work ..
therefore B does 1-2/5=3/5 work.. 
Also in 24 minutes B can print 5*24=120 pages..
so 120=(3/5-2/5) of total work..
so 1/5 of total work = 120..
 or total work = 600 pages..

2) 1/a + 1/b = 1/24..
1/60 + 1/b = 1/24..
b=40 minutes..
total work = 24(A+B)=24(A+A+5)=48A+120..
A's work individually= 60A..
so 60A=48A+120..
A=10..
so total pages = 60A=600..

shasadou · Answer

Hi Bunuel

Can we solve this using weighted average approach? I am actually stuck at some point: so we derive that the faster machine B takes 40 minutes to complete the job. That is 20 minutes faster (can we come to solution from here somehow given that in 20 minutes B will print 100 pages more) that A alone.

Then I draw the weighted average line and get that: a/b = 16/36 = 4/9. I am trying to plug in further a/(a+5) = 9/4. But I dont get the answer and get stuck. Can you help please?

shasadou · Answer

thanks! but we do not need this calculation in the 2nd method, do we?

2) 1/a + 1/b = 1/24..
1/60 + 1/b = 1/24..
b=40 minutes..

shasadou · Answer

yeah, i intuitively wanted to solve this way! thanks
 1) both finish the work in 24 minutes..
so A does 24/60=2/5 work ..
therefore B does 1-2/5=3/5 work..
Also in 24 minutes B can print 5*24=120 pages..
so 120=(3/5-2/5) of total work..
so 1/5 of total work = 120..
or total work = 600 pages..

please confirm whether my reasoning is right: A takes 60 min alone and B - 40 mins. Hence we can see how their productivity relates to each other: 40/60 = 2/3. This means taken together A performs 2/5 of the job and B - 3/5. Therefore the difference in the work done between A and B is simply 1/5.

1/5 w = 120 pages. Hence full work = 600!

chetan2u · Answer

Hi,
yes you are right .
it is not required here. but can be used in another method..
B does in 40 min and A in 60 min..
In these 40 minutes B does 5*40=200 more than A..
A completes these 200 in next 20 minutes, 
so speed =200 in 20= 10 in 1 min...
in 60 minutes = 10*60=600..

dharan · Answer

It requires two steps.
1. Calculate the number of hours B involves in finishing the task
2. Equate the rates of both A and B w.r.t total job or total pages in this case

Step 1  : 
We all know

1/A + 1/B = 1/24 min
=> 1/60 + 1/B = 1/24 with this we get B = 40 mins

Step 2:

It is said that B prints 5 pages more than A. And we know  rate = jobs /time

So let "j" be the total number of pages to be printed. 
Then the (rate of ) B = ( rate of ) A + 5
=> j /40 = j /60 + 5
calculating for j we get 600.

SchruteDwight · Answer

Good question

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

anish0953 · Answer

Very easy explaination , thanks for this

VikramMarkiv · Answer

Do let me know if the thought process here is correct.

Let us assume the document has x pages. 
Then rate of (A+B) = x/24 (pages/min)
Rate of A = x /60 (pages/min)
Rate of B = x/60 + 5 (pages/min) or (x+300)/60

Rate of A + Rate of B = Rate of (A+B)
x/60 + (x+300)/60 = x/24
On solving x = 600 pages.

Matteo13120 · Answer

I did it like that
1/60+1/T=1/24
T=40

r: number of page printed per minute
r=1/60
so 60r=1
and r+5=1/40
so 40r+200=1
and so 40r+200=60r
r=10
and so there is 60(10) pages to print so 600
don't know if this is correct

Bunuel · Answer

The red part is a bit unclear. Once you find that Printer B takes 40 minutes, you can set up the equation using their rates per minute. Let the document have p pages. Since B prints 5 pages more per minute than A:

p/60 = p/40 - 5

Solving this gives p = 600.

M23-16

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