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

B in a minute=x/40
A in a minute=x/60
then,
x/40-x/60=5

Solving x=600

You can denote rate directly by some variable (a in the solution) or express rate as a reciprocal of time. For example, say printer A needs t minutes to print 1 page and printer B needs m minutes to print 1 page, then the rate of printer A would be job/time=1/t pages per minute and the rate of printer B would be 1/m pages per minute (rate is a reciprocal of time, so 1/t=a and 1/m=b). In this case the equation would be 24(1/t+1/m)=x.

Hope it's clear.
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\(\frac{1}{A}=\frac{1}{60}\)
\(\frac{1}{B}+\frac{1}{A}=\frac{1}{24}\)

Get: \(\frac{1}{B}\)

\(\frac{1}{B}=\frac{1}{24}-\frac{1}{60}=\frac{1}{40}\)

Let p be the number of pages produced by A.
Let p+5 be the number of pages produced by B.

\(24(p + p+5) = 60(p)==> p=10pages\)

Answer: 60(p)=600pages

Ta = 60min
Ra = 1/Ta = 1/60
Rb = 1/Tb

Combined task completion time 24min.
=Ra + Rb
=1/60 + 1/Tb = 1/24
Tb = 40 min.

Ra = X/Ta Rb = X/Tb

Ra + 5 = Rb
X/Ta + 5 = X/Tb
X/60 + 5 = X/40
X=600 Ans.

I'm curious about the 1/a+1/b=1/24 solution as well. I started out trying that way and got stuck at the same point as the other fellow. Is there any way to solve it once you have 1/60+1/40 for their combined rates? Or is that just a dead end?


edit: Also, question #2:

Shouldn't the equation be 24(1/a+1/b)=x; ? Since you have 24 minutes in which the machines are working at their individual rates, doing 1/a and 1/b of the job per minute? I don't get how one can know when to arbitrarily use "a" instead of '1/a" or "b" instead of "1/b"

Rate A= X
Rate B= X+5

Work(A)=> X * 60 = 60X

Rate(A+B) * 24 = Work

(2X+5) * 24 = 60X

X=10

Easiest way to do this: Machine A and B can do the task in 24 minutes thus Rate of A and B = 1/24. Now given A can do the task in 60 minutes therefore Rate of A= 1/60. We know that Rate of A and B = Rate of A + Rate of B therefore Rate of B= Rate of A and B - Rate of A = 1/24-1/60= 1/40. Now we know that Rate of B = 1/40 thus B can do the work in 40 minutes.

Let pages printed per minute by A = x, given that pages printed by B per minute is 5 more than that of A
Pages printed by B per minute = x+5
Now Complete task is done by A in 60 minutes therefore total number of pages printed by A = x * 60
Also Complete task is done by B in 40 minutes therefore total number of pages printed by B = (x+5) * 40
therefore x * 60 = (x+5) * 40
therefore x=10
thus the total number of pages in task = x*60 = 10*60 = 600

Another approach after getting rate for B
as rate of B = 1/40
let A prints x pages a minute , then B will print x+5pages a minute
A work for 60 minutes and B work for 40 minutes alone and so ,they are able to print same no. of pages
thus,
40(x+5) = 60x
40x+200 =60x
20x=200
x=10
thus total no of pages = 60x or 40(x+5) =600 pages
Ans A

Let the total work be 120 units

So, Efficiency of A and B is 5 units/min & Efficiency of A is 2 units/min

Thus , the efficiency of B is 3 units/min

So, 1unit/min = 5 Pages

Hence, 120 Units = 120*5 => 600 Units, Answer must be (A)
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