Tap A can fill a tank in 36 minutes, Tap B can fill the same

Question

Tap A can fill a tank in 36 minutes, Tap B can fill the same tank in 48 minutes. If they are opened simultaneously, at what time tap B (keep tap A running) can be stopped so that the tank can be filled completely filled in 27 minutes.

A. 8
B. 12
C. 20
D. 30
E. 36

This question was asked by one of the tutor who was giving presentation on a local GMAT prep course.I cannot remember the options exactly, but all options were integers. I guess b/w (12-40).If the question sounds awkward or has other flaws please feel free to provide inputs/correct it.I am looking for its solution and similar rate problems in which 2 entities work together for some portion and then one of 'em leaves.

abhishekkpv · Accepted Answer

Tap A can fill a tank in 36 minutes which means that 1/36th of the tank will be filled up in a minute
Tap B can fill a tank in 48minutes which means that 1/48th of the tank will be filled up in a minute

and Given that A is open for 27 min --> 27/36 or 3/4 of the tank will be filled and B has to fill the remaing 1/4th of the tank.

B will fill the enitre tank in 48 mins and for it to fill 1/4 th of the tank it will take (48/4)12 mins.

mbaiseasy · Answer

Rate of B x time + Rate of A x 27 minutes = 1 (combined output of Tap A and B)
 \frac{1}{48} t + \frac{27}{36}= 1 
 \frac{1}{48} t = 1 - \frac{3}{4} 
 \frac{1}{48} t = \frac{1}{4}

t = 12 minutes

conty911 · Answer

Thanks that helps kudos to you .

honggil · Answer

You can also use two equations provided:
(1/36 + 1/48)t1 + (1/36)t2 =1
t1 + t2 = 27 -> t2 = 27 - t1

(1/36 + 1/48)t1 + (1/36)(27 - t1) = 1

t1 = 12

vrnr · Answer

A to be opened for 27 mins that is 27/36 =3/4 of the tank is filled..

so remaining 1/4th of tank to be filled by B

48 /4 = 12 mins to fill 1/4 of the remaining...(logic is 1/4 =x/48) !!

ChiranjeevSingh · Answer

Very good way of thinking. +1

Cheers,
CJ

grandtheman · Answer

I would approach this question in some other way, since it says that the taps are opened simultaneously, and the question asks what time tap B can be stopped at interval "after both taps have been opened for some time" so that the entire tank can be filled in 27 minutes ( not  running tap A for addition 27 minutes).

1. find the combined rate of two taps (since they are opened simultaneously): work/time>>> (1/36+1/48) = 6/144, meaning that combined rate is 144/6 = 24 minutes (both taps can fill up the tank in 24 minutes if with no pause on either tap).

2. let T be the time that tap B can be stopped. we can form the work formula letting a+b run together for T + tap A alone continues running for 27-T (since total time is 27 minutes) = 1 (filling up the tank)

the equation looks like this : (1/24)T + (1/36)(27-T) = 1
>>> 3T/72 +(54-2T)/72 = 1
solve this equation you will get T = 18 minutes, the time that tap B can be stopped so that tank can be filled in 27 minutes, which is the answer.

in this case, tap A alone will continue running for 9 minutes to fill up the tank.

Abhishek009 · Answer

Let the volume be = 144

Efficiency of A = 4
Efficiency of B = 3
Combinedd efficiency of A & B = 7

7*( 27 - t ) + 4t = 144

189 -7t + 4t = 144

Or, 3t = 45

So, t = 15

Thus tap B must be stopped after 12 ( ie, 27 - 15) minutes

bb · Answer

Added answer choices to the question. Thank you for reporting it.

Varun121595 · Answer

Tap A can fill a tank in 36 minutes, Tap B can fill the same tank in 48 minutes. If they are opened simultaneously, at what time tap B (keep tap A running) can be stopped so that the tank can be filled completely filled in 27 minutes.

A. 8
B. 12
C. 20
D. 30
E. 36

Ans. Let the volume be = 144

Efficiency of A = 4
Efficiency of B = 3

Tap A will run for 27 minutes so 27*4 = 108 units done
Remaining units will be done by B that is 36/3 = 12 minutes
Tap B will work for 12 minutes.

rajsinghudr · Answer

Your calculation is wrong at the first step:

(1/36+1/48) = 6/144
this is not right. 
 (1/36+1/48) = 7/144

So eventually you will also get 12 minutes as answer.
"Approaches can be different in maths, but the answer remains same."

pushpitkc · Answer

Hey rajsinghudr Appreciate the effort but grandtheman posted that post in 2012

Btw, Welcome to GMATClub. All the best with your GMAT journey!

fireagablast · Answer

1=(1/36 + 1/48)t1 + (1/36)t2
1= 1/36(t1+t2) + (1/48)t1
1= 1/36(27) + (1/48)t1
1= 27/48 + t1/48
1-27/48=t1/48
1/4 = t1/48
12 = t1

B

Rohit_842 · Answer

The question says taps A and B both are open simultaneously and B stops at some time and A continues to run. Meaning 1/4th of the remaining tank needs to be filled by both A and B.

Is there something I'm missing or are the options inconsistent with the question? Kindly help  Bunuel

Krunaal · Answer

Tap A runs for the whole 27 mins, while B stops at some point. So if it were only A running the 3/4th of the tank would've been filled but because B ran for a while that 1/4th of the space got filled.

Assume that capacity of the tank is 288 litres, then rate of tap A = 8 lt/min and rate of tap B = 6 lt/min, their rate working together will be 14 lt/min

Now tap A and tap B are both open for some period of time t

=> 14*t + 8*(27-t) = 288 ..............................(14*t is A and B working together, 8*(27-t) is only tap A working since we are given that total time should be 27 mins)
=>  t = 12

Thus, A and B will work together for 12 minutes, post which tap B can be stopped and only tap A runs.

muhammaddk92 · Answer

Combined rate is 7/144min. So combined they can finish one job in 1/21 mins. So answer has to be less than 21.

For 12 mins, combined they do 3/5 of the work. B alone can do the remainder 2/5 of the work in 15 mins. Hence B is the answer.

Rishm · Answer

Tap A can fill the tank in 2.77 efficiency and B is 2.1 efficieny. Tap A ran for 27 mins, hence 27*2.77 will be around 75, meaning 3/4 is already filled. Now 2.1 multiply by 12 comes as the closest point. Hence 12 is the answer

Tap A can fill a tank in 36 minutes, Tap B can fill the same

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Tap A can fill a tank in 36 minutes, Tap B can fill the same

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