Working together, printer A and printer B would finish the task in 24 minutes. Printer A alone would finish the task in 60 minutes. How many pages does the task contain if printer B prints 5 pages a minute more than printer A ?

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

POE approach :
we are given combined time= 24
ie combined rate per minute= 1/24

s the time here is an integer then the whole work must be divisible by 24 ...or we wont get an integer value
eliminate all the choices that are not divisible by 24 ...
choices B C E gone

between choices A and D i would straight away choose option A 600 because A takes only 60 minutes to complete the work... now even if you are not sure
try to divide with individual rates and you will see A is the answer choices

TAKEAWAY:
- Use POE when you are running out of time...the above appraoch took me less than 45 seconds... all you have to do is increase your probability of answering the Q correctly...your probability after eliminating 3 choices becomes 50%..
- thumbrule - the huge the amount of work the more the time required...as the time taken is not very considerable then so will the work be...not too great...

Trust me i try this appraoch when I'm at 28th Q , and have to rush...i use this this appraoch n guess what i alnost get 50% answers right...thats better than answering just 1 right and randomly guessing other

In this case we'd have:
The rate of printer A = 1/a pages per minute, where a is the time to print 1 page.
The rate of printer B = 1/b pages per minute, where b is the time to print 1 page.

Working together, printer A and printer B would finish the task in 24 minutes" --> \(24(\frac{1}{a}+\frac{1}{b})=x\);
Printer A alone would finish the task in 60 minutes --> \(60*\frac{1}{a}=x\);
Printer B prints 5 pages a minute more than printer A --> \(\frac{1}{b}=\frac{1}{a}+5\).

Solving for \(x\) --> \(x=600\).

Answer: A.[/quote]

Can I get some help please? In some questions, we put the completed task as "1" however in this case we put the pages (completed task) as x... why is that the case? How can i know when to use "1" and when to use a variable?

1/A + 1/B = 1/24
A=60.

Find B. B=40.

60*x = 40*(x+5) where x is no of pages printed by A in a minute.
x=10
Hence number of pages = 600.

Please kudos.

Solution:

We can let x = the number of minutes it takes printer B to finish the task by itself and create the equation:

1/60 + 1/x = 1/24

Multiplying both sides of the equation by 120x, we have:

2x+ 120 = 5x

120 = 3x

40 = x

Now, if we let n = the total number of pages the task has and since printer B prints 5 pages a minute more than printer A, we can recreate the equation:

n/60 + 5 = n/40

Multiplying both sides of the equation by 120, we have:

2n + 600 = 3n

600 = n

Answer: A
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Hi Bunuel,

I Have gone through your solutions of all the similar problems and what I have observed is that for some, you begin with assuming variables for time taken (eg. time taken is a for Machine A and b for Machine B), whereas for others you begin with assuming variables for the rate of work (eg. Rate for Machine A is a and Rate for Machine B is b)

IS there any specific reasoning/logic to begin the questions in one of the either ways?

Your explanation would be really helpful.

Thanks

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