Pipe A and Pipe B fill water into a tank of capacity 1000 litres at

Question

Pipe A and Pipe B fill water into a tank of capacity 1000 litres at the rate of 100 litres/minute and 25 litres/minute respectively. Pipe C drains water from the same tank at the rate of 50litres/minute. Pipe A is kept open for a minute and then closed, then pipe B is kept open for a minute and then closed, followed by a drain pipe C for a minute and then closed. This process is repeated until the tank is full. How long will it take to fill the tank.
A) 39 mins
B) 40 mins
C) 39 mins and 20 secs
D) 37 mins
E) 41 mins

Source: 4gmat

I am getting B

Can you tell me where I am going wrong

A) 39 mins
B) 40 mins
C) 39 mins and 20 secs
D) 37 mins
E) 41 mins

Source: 4gmat

eshan429 · Accepted Answer

At time 0 minutes, water in the tank = 0 liters

At time 1 minute, water in the tank = 100 liters (0 from before + 100 from pipe A)

At time 2 minutes, water in the tank = 125 liters (100 from before + 25 from pipe B)

At time 3 minutes, water in the tank = 75 liters (125 from before - 50 from pipe C)

If we take these steps as one single step.

At time 6 minutes, water in the tank = 150 liters (75 from before + 75 from the new round)

Now, we can see that after 6*6 = 36 minutes, water in the tank = 150 * 6= 900 liters

Now, since we start the process over again, At time 37 minutes, water in the tank = 1000 liters (900 from before + 100 from pipe A)

Hence D

Hope that makes it clear

DmitryFarberMPrep · Answer

To address B, here's where I'm guessing you went wrong:

Like eshan429, you put all 3 together as a 3-minute cycle that adds 75 liters. You divided 1000 by 75 and saw that you got 13 full cycles, for a total volume of 975. Clearly the next minute (+100) would put you over 1000, so the total time seemed to be 40. Right?

The problem with this solution is that it glosses over the fact that we just dropped *down* from 1025 to 975. From here, you'd have to notice that you could actually go  backward  from 39 minutes to 37 and hit 1000.

Bunuel · Answer

Similar question to practice: pipe-a-fills-a-tank-of-capacity-700-liters-at-the-rate-of-93482.html

DebWenger · Answer

A generic method to solve such questions would be:
As has been stated in some earlier posts volume of water in the tank increases by 75l every 3 mins.
Then 1000/75=40/3 cycles of 3 mins.Hence 40/3 *3=40 mins

At this juncture we take the 3 min cycle prior to reaching 40 mins-> 40-3=37mins
Divide 37/3->12th cycle,In each cycle volume of water increases by 75,so in 12 cycles it leads to 12*75=900l
Clearly to reach 1000l we need another 100l.This balance volume will be filled up by tap A in the next 1 min as its rate is 100 l/min.
Thus,12*3 +1 min=37mins

Hope this helps us to solve such questions.
Let me know what you guys at GC think!

sanket1991 · Answer

the process is 1st minute 100 ltrs fill 2nd minutes 25 litres fill 3rd minute 25litres emptying you are taking 75ltrs/ 3mins and calculating accordingly till 36th minute calculation is perfect, however question asks at what time tank will fill completely. and on 36th minute tank fills upto 900litres. On 37th minutes tank will fill more by 100 liters; so total goes to 1000 litres. and hekce the answer.

guialain · Answer

Every 3 min the tank gets filled with (100+25-50) liters, which is 75 liters
After 36 minutes the tank is filled with 900 liters (=12*75 liters).
the remaining 100 liters are filled by pipe A in 1 min, and that's it!

So answer is 37 mins

LeonidK · Answer

Pipe A and B increase amount of water in the tank
Pipe C - decreased

After 3 minutes:
+100 l (1 minute of work of pipe A) + 25l (1 minute of work of pipe B) - 50 l (1 minute of work pipe C) = +75 liters

After 36 min (12 full cycles) = 75*12 = 900
+1 minute = +100 l

So answer 37 min

Mahmud6 · Answer

Why the followings are wrong?

75 ltr in 3 min
1 ltr in 3/75 min
1000 ltr in (3*1000)/75 = 40 min.

OR

75 ltr in 1 3 min cycle
1 ltr in 1/75 3 min cycle
1000 ltr in (1*1000)/75 = 13.33 3 min cycle => 13.33*3=39.99 min

OR

In 3 min ----75 ltr 
In 1 min ---- 75/3 ltr
In 39 min ---- (75*39)/3=975 liter

1000-975=25 ltr
Pipe A 100 litr in 60 sec => 25 lit in 15 sec

So, total time taken is 39 min 15 sec.

DmitryFarberMPrep · Answer

Mahmud6 , read the first two responses from eshan429 and me. Basically, you overlooked the fact that the end of the 3-minute cycle brings the volume  lower , so it reaches 1,000 earlier than you predicted and then has to refill to get there again.

vinayyadav512 · Answer

Every 3 min tank filled is 100+25-50= 75 liters

Now , In 36 min tank would be filled 36*75/3= 900 liters
NOW, IN ANOTHER ONE MINUTE PIPE A WILL FILL 100 LITERS AND THUS FILL THE TANK AS WELL
THEREFORE,37 MIN IN TOTAL

Posted from my mobile device

Archit3110 · Answer

total net flow rate in and outflow will given ; 100+25-50 ; 75 ltrs /min
so for every 3 mins filled tank is 25 ltrs 
so in 36 mins 25*36 ; 900 ltrs 
+ 1 min for tank A ; 100 ltrs ; 1000 ltrs
36+1 ; 37 mins
IMO D

JoyantaMitra · Answer

c is the answer
975/75=13 so 13*3=39 min + (25/100) min what is the problem here?

Nabneet · Answer

The issue is, after 12 attempts (each cycle =3mins) the tank will be 75*12 =900lts full

Then in next 1min, only pipe A operates and fills out the remaining100lts

So total time will be 12*3 +1 =37mins

bumpbot · Answer

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Pipe A and Pipe B fill water into a tank of capacity 1000 litres at

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