Hello Everyone,
Today I just happened to come across a work and time problem, which had a 95% difficulty level. I immediately thought of a way to do it and realized two ways were already discussed but not this one. All three would fall into category of standard methods.
This prompted me to see if a fourth method could be found, a POE(Process Of Elimination) method. And I realized it was faster and brought down the difficulty level by a bit of thinking.The point is a bit of thinking can actually give us clues to try to solve the Qs in lesser time and different ways. But its important for that to try out different methods when we are practicing.
Here I will touch upon all 4 methods that can be used to solve the Q.
I would prefer
POE if the choices have values spread apart, otherwise any of the remaining three.Question is:-It takes printer A 4 more minutes than printer B to print 40 pages. Working together, the two printers can print 50 pages in 6 minutes. How long will it take printer A to print 80 pages?
A. 12
B. 18
C. 20
D. 24
E. 30
1)
POE..
yes, you can use the method of elimination to get to the answer...
what do we do?..
. we try and find the MINIMUM and MAXIMUM value it can take and then check for the choices..first step:-
combined both do 50 pages in 6 minutes.
80 pages can be done in 6*80/50=48/5= 9 minutes 36 seconds..
second step:-
If there is a difference of 4 minutes while doing 40 pages, the difference will increase to 8 minutes for 80 pages..
We have one slower,A and one faster, B...
A and B do 80 pages in 9min 36 secs..
Both will do 2times 80 pages in 19 min 12 secs...
2 of As will do 2 times 80 pages in > 19 min 12 secs,A works with a faster machine to clock a time of 19 min 36 secs...
or A will do 1 time 80 pages >19 min 12 secs..so 19 min 12 secs becomes our min time if the two A and B operate at the same speed..,
but ofcourse it should be much more, since there is a 8 minutes diff between the two....
this eliminates all except 24 and 30..third step:-
lets find the max it can be ..the difference between A and B is 8 min..
B is faster than A, so should take less their combined time 19 min 12 secs...
Although A will be lesser than but, in no way, it can go beyond 19 min 12 secs. + 8 min, if we take B as 19 min 12 secs, the max possible (we are taking this,although in reality it will be lesser to check max value of A).
so max time = 19 min 12 secs. + 8 min = 27 min 12 secs..this eliminates 30 too..
ans 24 min...
2)
Second method
We can work on 50 pages and 6 min as there are two values avail..
there is a difference of 4 mins in 40 pages..
so, there will be a difference of 5 mins in 50 pages..
let the time taken by A be x min, then B will take x-5 min..
their combined one minute work= 50/x + 50/(x-5)...
combined they do 50 pages in 6 min, so they will do 50/6 in one minute..
so \(\frac{50}{x} + \frac{50}{{x-5}} = \frac{50}{6}\)..
removing 50 from both sides \(6x-30 + 6x= x^2-5x\)...
x^2-17x+30 =0.....
x=15 or -2...
it cannot be negative, therefore x=15..
now A does 50 pages in 15 min, so it will do 80 pages in 15*80/50 = 24 min..
3)
Another Standard method
(I am copying from the earlier post, so thanks @Bunuel)
Quote:
Let the time needed to print 40 pages for printer A be \(a\) minutes, so for printer B it would be \(a-4\) minutes.
The rate of A would be \(rate=\frac{job}{time}=\frac{40}{a}\) pages per minute and the rate of B \(rate=\frac{job}{time}=\frac{40}{a-4}\) pages per minute.
Their combined rate would be \(\frac{40}{a}+\frac{40}{a-4}\) pages per minute. Also as "two printers can print 50 pages in 6 minutes" then their combined rate is \(rate=\frac{job}{time}=\frac{50}{6}\), so \(\frac{40}{a}+\frac{40}{a-4}=\frac{50}{6}\).
\(\frac{40}{a}+\frac{40}{a-4}=\frac{50}{6}\) --> \(\frac{1}{a}+\frac{1}{a-4}=\frac{5}{24}\). At this point we can either try to substitute the values from answer choices or solve quadratic equation. Remember as we are asked to find time needed for printer A to print \(80\) pages, then the answer would be \(2a\) (as \(a\) is the time needed to print \(40\) pages). Answer D works: \(2a=24\) --> \(a=12\) --> \(\frac{1}{12}+\frac{1}{8}=\frac{5}{24}\).
4)
another way in the same thread
..
We need time taken by printer A to print 80 pages. (Let's say this is 'a' mins)
We know A takes 4 more mins for 40 pages so it will take 8 more minutes for 80 pages.
Together, they print 50 pages in 6 mins so they will print 80 pages in 6*50/80 = 48/5 mins
Now, make your sum of rates equation:
1/a + 1/(a - 8) = 5/48
Now look at the options and substitute here. First check out the straight forward options.
Say, a = 12
1/12 + 1/4 = 4/12 Nope
I will not try 18 and 20 because (18, 10) and (20, 12) doesn't give me 48, the denominator on right hand side.
I will try 24 instead.
1/24 + 1/16 = 5/48 Yes.
Answer is 24...
Finer points
1. there can be various methods to solve the Qs, by substitution, by standard algebra, or by POE..
2. we have to see how each fits in, but these have to be practiced in abundance to get a feel of each method.