Three pipes, A, B and C are opened to fill an empty tank such that A

Question

Three pipes, A, B and C are opened to fill an empty tank such that A and B cam fill the tank alone in 36 minutes and 45 minutes respectively and C can empty it in 30 minutes. After 6 minutes the emptying pipe is closed. In how many minutes the tank will be filled ?

A. 18
B. 20
C. 24
D. 25
E. 30

A. 18
B. 20
C. 24
D. 25
E. 30

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ThatDudeKnows · Accepted Answer

Is there some piece of information that would make solving this question a lot less annoying? What if we just knew how many gallons the tank is? Let's make something up! With 36, 45 and 30, 180 feels like a good number.

A fills 180 gallons in 36 minutes, so +5 gallons per minute.
B fills 180 gallons in 45 minutes, so +4 gallons per minute. 
C empties 180 gallons in 30 minutes, so -6 gallons per minute.

All three combine to fill 5+4-6 = 3 gallons per minute, so that's 18 gallons in 6 minutes.

We still have 162 gallons to fill. A and B fill at a combined +9 gallons per minute, which means it takes 162/9 = 18 additional minutes.

At this point, the question is ambiguous as to whether it is asking for the number of minutes that A and B work alone after C is closed (which would be 18), or for the total number of minutes including when C was open (which would be 18+6 = 24)...I'll assume the former, but it would be good if the question were edited to eliminate the ambiguity.

Answer choice A.

That missing piece of information trick makes this what I call a "Hidden Plug In" question. There's no variable that I plugged in for, but there's some piece of information that allows us to work with actual numbers (and integers, to boot) rather than percentages or fractions of a whole. Rather than working with percentages or fractions of a whole, just make up a number to represent the whole and go from there. The most common applications are work/job (including fill/empty), though there are other opportunities, as well.

ThatDudeKnowsHiddenPlugIn

hinasingh · Answer

Three pipes, A, B and C are opened to fill an empty tank such that A and B cam fill the tank alone in 36 minutes and 45 minutes respectively and C can empty it in 30 minutes. After 6 minutes the emptying pipe is closed. In how many minutes the tank will be filled?
Let W be the capacity of tank
A and B cam fill the tank alone in 36 minutes and 45 minutes respectively
So, together they will take (1/36 + 1/45 = 1/20) 20 mins
Now the pipe C(30 mins to empty W => in 6 mins it can empty W/5 portion of tank) was kept ON for 6 mins => it has emptied W/5 portion of tank
So, the pipes A and B need to fill the extra W/5 portion 
for which they need another 4 mins
Hence, in total they need 20 + 4 = 24 mins.
Answer C

MBAHOUSE · Answer

Three pipes, A, B and C are opened to fill an empty tank such that A and B cam fill the tank alone in 36 minutes and 45 minutes respectively and C can empty it in 30 minutes. After 6 minutes the emptying pipe is closed. In how many minutes the tank will be filled ?

A. 18
B. 20
C. 24
D. 25
E. 30

SaquibHGMATWhiz · Answer

Solution: Let the work be 180 (LCM of 36, 45 and 30) Rate of A =\frac{Work}{Time}=\frac{180}{36}=5 Rate of B =\frac{Work}{Time}=\frac{180}{45}=4 Rate of C =\frac{Work}{Time}=\frac{180}{30}=-6 (negative because pipe C is used to empty the tank) Let the time needed to fill the tank be t mins wrtt.png According to the question, 5t+4t-36=180 or t=24 Hence the right answer is Option C

pramodmundhra15 · Answer

What has been asked is ambiguous, rightly pointed out by  ThatDudeKnows

joseph1104 · Answer

I followed the same approach . However you'll also need to add the additional 6 mins to 18. Hence total time is T = 6+18 = 24 mins.

bumpbot · Answer

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Three pipes, A, B and C are opened to fill an empty tank such that A

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GMAT Problem Solving (PS) Questions

Three pipes, A, B and C are opened to fill an empty tank such that A

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