printer A and printer B

[nhai2003]

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 ?
1:600
2:800
3:1000
4:1200
5:1500


Help me!

[brick2009]

The answer should be : A

A+B = x/24 pages/min
A = x/60 pages/min
B = (x/60 + 5) pages/min

x/24 = x/60 + (x/60 + 5)
x/24 - 2x/60 = 5
Solve for X , X = 600

[nitya34]

good one.Thanks

we can calculate,B alone can do in 40 mins


Now say its 600

A--10(60)=600

B---15(40)=600

Together--25(24)=600

[samirnajeeb]

time taken by A & B working together = a*b/(a+b)

60b/(60+b)=24
b=40
b takes 40mins to complete the task

B in a minute=x/40
A in a minute=x/60

x/40-x/60=5

x=600

[GMATGuruNY]

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 ?
1:600
2:800
3:1000
4:1200
5:1500


Help me!

We can plug in the answer choices, which represent the number of pages. The correct answer choice will be divisible by 24 and 60. Eliminate B, C and E.

Answer choice A: 600 pages
Combined rate for A+B = w/t = 600/24 = 25 pages per minute.
Rate for A alone = w/t = 600/60 = 10 pages per minute.
Rate for B alone = Combined rate - A alone = 25-10 = 15 pages per minute.
Difference between B and A = 15-10 = 5 pages per minute. Success!

The correct answer is A.

[mcdesty]

Rate Time Distance
Printer A a/60 60 a (Question then becomes what is A?)

Printer B (a/60)+5 (B prints 5 pages a minute more than printer A)

Together = a/60 + (a/60)+5
= a/60 + (a/60) + (300/60) (Same as 5)
= a/60 + (300 + a)/60 (Add them now as they have a common denominator)
= (2a + 300)/60 (Combined Rate)
= a/(2a + 300)/60 = 24 (This is how we got 24;By dividing the distance/combined rate)
= 60a = 24(2a +300) (Algebra, be careful here!!)
= 60a - 48a= 24(300) (Do not simplify until the very end:You just waste time by doing so)
= a= 600
I think this is faster!

[GMAT Kolaveri]

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 ?
1:600
2:800
3:1000
4:1200
5:1500


Help me!

AO must be multiple of 60. (bcoz d combined time taken is a whole number)

Lets start with 600 (on actual GMAT its better to start with B or D rather than starting with extremes A or D)

A= 600/60 = 10 units of work
B= 10+ 5= 15 units of work

combined units of work done in a minute = 25 (10+15 A+B)
Combined Time taken = total work/combined rate = 600/25 = 24 which is given in the question. Hence AO= A.

GMAT Quant tip on work rate:
Always assume the work done as LCM of the individual rates.
Benefits:
1. Avoid fractions in calculations and hence avoid calculation mistakes.
2. Saves few seconds. (do not undermine the few seconds saved on EACH Question)

[Scott@TargetTestPrep]

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 ?
1:600
2:800
3:1000
4:1200
5:1500


Help me!

We can let x = the number of pages printer A can print per minute; thus x + 5 = the number of pages printer B can print per minute.

Since printer A can finish the task by itself in 60 minutes, the task has 60x pages. Since printers A and B together can finish the task in 24 minutes, we can create the equation:

24x + 24(x + 5) = 60x

24x + 24x + 120 = 60x

48x + 120 = 60x

120 = 12x

10 = x

Therefore, the task has 60(10) = 600 pages.

Alternate Solution:

Let printer B finish the task alone in x minutes. Then, 1/60 + 1/x = 1/24. Solving for x, we get 1/x = 1/24 - 1/60 = 5/120 - 2/120 = 3/120 = 1/40. Thus, x = 40, i.e., it takes printer B 40 minutes to complete the task.

Let n be the total number of pages to be printed. Then, printer A prints n/60 pages per minute and printer B prints n/40 pages per minute. We are told that the latter is 5 greater than the former; therefore:

n/40 - n/60 = 5

3n/120 - 2n/120 = 5

n/120 = 5

n = 600

So, the task contains 600 pages.

Answer: A

[Mehwish01]

Answer:

total time taken by B = 24 * 60 / (60 -24) = 40 min.

A take 60 min. B takes 40 min to complete a task.

Now, divide the values given in option (in Ans) to get the rate per min.

option A: 600 / 10 = 60 & 600/40 = 15 > this satisfies the condition given in question stem that printer B prints 5 pages a minute more than printer A ?

. therefore A

Step-by-step explanation:

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.

[carryon]

The answer should be 1.