Pipe A fills a tank at the rate of 100lit/min, Pipe B fills a tank at

Question

Pipe A fills a tank at the rate of 100lit/min, Pipe B fills a tank at the rate of 25 lit/min, and pipe C drains a tank at the rate of 50 lit/min. First pipe B is opened for 1 minute and then closed, after that pipe C is opened for 1 minute and then closed, after that pipe A is opened for 1 minute and then closed. If this continues till a 7000-litre empty tank is filled to the capacity, how long will it take to fill the tank ?

A. 276 minutes
B. 277 minutes
C. 278 minutes
D. 279 minutes
E. 280 minutes

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yashikaaggarwal · Answer

Answer should be 279 minutes.
First B pipe is opened for 1 min filling 25 litre
Then C pipe is opened for 1 min draining 25 litre ( since only 25 litre was present in starting)
The Pipe A is opened for 1 min and it filled 100.
Repeating the process will lead to (100+25-50+100)=175 litres.
That MEANS from the second time onwards pipes will fill 75 litre in 3 min.
25 litre in 1 min.
So 6900 litre tank (7000-100 as 100 is already filled in first attempt) will be filled in 6900/25= 276 + 3 minutes from the initial process. = 279

Answer is supposedly D

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lacktutor · Answer

hi,  yashikaaggarwal 
why didn't you add the first 3 minutes (from the first attempt as you said above ) to 276 ?
Shouldn't it be 276+3 = 279 minutes ?

yashikaaggarwal · Answer

Yeah. I got my mistake

TamirKalderon · Answer

Why does it say the answer is E?

saynchalk · Answer

I wanted to go for the straightforward method but was worried that I might be wrong. However, the straightforward method is the right one as per OA.

A = +100 litres / min
B = +25 litres / min
C = -50 litres / min

Every 3 mins = +75 litres
Every 1 min = 25 litres = Combined rate

Work = 7000 litres

W = Rate * T

T =  W / R
T = 7000 / 25
T = 280 minutes

TamirKalderon · Answer

That's fine except for the fact that after the first 3 minutes there's actually 100 literes in the tank and not 75... So the answer should be 279 Double checked it with excel https://gmatclub.com/forum/download/file.php?id=81948 GMAT-Club-Forum-bkgidxaz.png

TamirKalderon · Answer

That's fine except for the fact that after the first 3 minutes there's actually 100 literes in the tank and not 75... So the answer should be 279 Double checked it with excel https://gmatclub.com/forum/download/file.php?id=81949 GMAT-Club-Forum-6dry3m44.png

onlyPlanA · Answer

I solved it like this:

First B is opened = 25 lt is filled
Then C is opened = 50 lt is emptied
Then A is opened = 100 lt is added.

So, the process (25-50+100) repeats x times to fill 7000 lt tank.
Hence, 75x = 7000
x = 280/3

But remember, this whole process takes 3 mins to complete one round.
So, total time = (280/3) * 3 = 280 mins.

Answer is E.

suntprovident · Answer

The OA should be D - in the first round 100 litres is filled due to the sequence being B, C and A

Bunuel  request you to please check if OA is correct or what are we missing ?

onlyPlanA · Answer

IMO, why the answer is not D is because even though 100 litres are filled in the first round, this volume does not stay constant throughout the entire process. So, it is not certain that after first round, 7000-100 = 6900 litres need to be filled. The volume is repeatedly changing because another pipe is draining the water simultaneously.

For example:
In first round, after 3 minutes, 100 litres of tank is filled. But in the second round, after 5 minutes, when pipe B and C are opened and closed, only 75 litres of water remains in the tank. In the 6th minute, the volume grows to 175lt. Hence, volume is constantly changing.

Like this:

First round = +25-50+100 = 100 (After 3 minutes)
Second round = 100+25-50 = 75 (After 2 minutes, that is total 5 minutes); then 75+100 = 175 (After 3rd minute of second round, that is total 6 minutes)

Thats why, we have to calculate using rounds, not volume. Hope I am making sense. But yes, I also wish to see the official explanation.

sharifalam · Answer

@Bunuel

Pipe A fills a tank at the rate of 100lit/min, Pipe B fills a tank at

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