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Tap A can fill a tank in 10hrs,Tap B can fill it in 20hrs, and an out

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Tap A can fill a tank in 10hrs,Tap B can fill it in 20hrs, and an out [#permalink]

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New post 22 Nov 2017, 13:28
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A
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Difficulty:

  65% (hard)

Question Stats:

68% (01:59) correct 32% (02:49) wrong based on 92 sessions

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Tap A can fill a tank in 10hrs,Tap B can fill it in 20hrs, and an outlet,Tap C can empty the tank in 30hrs. Each tap is opened,one by one,for exactly one hr and then closed. If its 7AM,the tank is 1/4th full and taps work in alphabetic order(A then B and then C),at what time will the tank begin to overflow?

1. 1:30 AM next day
2. 12PM
3. 8AM
4. 10AM
5. 5PM

Source:Experts' Global
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Tap A can fill a tank in 10hrs,Tap B can fill it in 20hrs, and an out [#permalink]

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New post 22 Nov 2017, 13:47
1
Assume capacity of the tank is 600 units.

The rate of filling the taps by Tap A is 60 units/hr, Tap B is 30 units/hr,
and Tap C empties the tank at the rate of 20 units/hr

At 7 AM, the tank is 1/4th full, hence we have 150 units of water.

Every 3 hours, the first two taps fill 90 units and in the third hour, the Tap C empties the
tank by 20 units. Therefore, in 3 hours, the tank is filled with 70 units of water.
So in 18 hours, the tap fills about 420 units of the remaining 450 units. The time is now 1 AM

Now as the Tap A starts filling up the tank, half an hour later, the tank is full and starts overflowing.
Therefore, the time when the tank starts overflowing is 1:30 AM next day(Option A)
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Re: Tap A can fill a tank in 10hrs,Tap B can fill it in 20hrs, and an out [#permalink]

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New post 23 Nov 2017, 09:53
I choose the hardest path:

Ra=1/10 Rb=1/20 Rc=1/30 and the container full of 1/4
so...
Ra=6/60 Rb=3/60 Rc=2/60 and the container full of 15/60

The following numbers represent the quantity of water present in the container in the various moments.

21 24 22 28 31 29 35 38 36 42 45 43 49 52 50 56 59 57 so... 7am + 18hrs = 1am next day, so the only possible answer is A!

It took me almost 5 minutes :(
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Tap A can fill a tank in 10hrs,Tap B can fill it in 20hrs, and an out [#permalink]

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New post Updated on: 30 Nov 2017, 18:41
The rate of tap A: 1/10. Tap B: 1/20. Tap C: 1/30 (outlet)

Each tap is opened one by one in 1 hour.
=> in 3h three taps can fill: 1/10 + 1/20 - 1/30 = 7/60 of the tank => rate = 7/60 : 3 = 7/180

7am : 1/4 of the tank
=> 3/4 of the tank till the tank full
Time needed = work/rate = 3/4 : 7/180 = 135/7 hours = 19 hours + around 20 minutes

=> Time the tank will begin to overflow = 7 + 19,2h = 1:30am next morning
=> A

Please correct me if I'm wrong!

Originally posted by lichting on 30 Nov 2017, 09:53.
Last edited by lichting on 30 Nov 2017, 18:41, edited 1 time in total.
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Tap A can fill a tank in 10hrs,Tap B can fill it in 20hrs, and an out [#permalink]

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New post 30 Nov 2017, 12:30
1
Sangeeta2018 wrote:
Tap A can fill a tank in 10hrs,Tap B can fill it in 20hrs, and an outlet,Tap C can empty the tank in 30hrs. Each tap is opened,one by one,for exactly one hr and then closed. If its 7AM,the tank is 1/4th full and taps work in alphabetic order(A then B and then C),at what time will the tank begin to overflow?

1. 1:30 AM next day
2. 12PM
3. 8AM
4. 10AM
5. 5PM

Source:Experts' Global



Let the size of the tank be 60.

Tap A fills @ 60/10 per hour = 6 per hour

Tap B fills @ 60/20 per hour = 3 per hour

Tap C empties @60/30 per hour = 2 per hour.

If these taps are opened in the order A, B and C for one hour each, then in 3 hours, the three taps can fill = 6 + 3 - 2 = 7

At 7 AM, the tank is 1/4th full, that means, we need to fill 3/4th of the tank.

3/4th of tank = 3/4 * 60 = 45

In 3 hours, the three taps can fill 7, thus in (6*3 = 18 hours), they can fill 7*6 = 42 units.

The remaining 3 units will be filled by A in half n hour (3/6 = 1/2 per hour)

Thus, the total time taken to fill the tank = 18.5 hours.

The tank would overflow after = 7 AM + 18.5 hours = 1:30 AM next day.


Correct Answer: Option A
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Tap A can fill a tank in 10hrs,Tap B can fill it in 20hrs, and an out [#permalink]

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New post 30 Nov 2017, 22:49
Sangeeta2018 wrote:
Tap A can fill a tank in 10hrs,Tap B can fill it in 20hrs, and an outlet,Tap C can empty the tank in 30hrs. Each tap is opened,one by one,for exactly one hr and then closed. If its 7AM,the tank is 1/4th full and taps work in alphabetic order(A then B and then C),at what time will the tank begin to overflow?

1. 1:30 AM next day
2. 12PM
3. 8AM
4. 10AM
5. 5PM

Source:Experts' Global


in each 3 hour cycle, 1/10+1/20-1/30=7/60 of the tank is filled
3/4, or 45/60, of the tank needs to be filled
after 6 cycles, or 18 hours, at 1 AM next day, 6*7/60=42/60 of the tank has been filled,
leaving 3/60 to be filled
(3/60)/(1/10)=1/2 hour more needed from Tap A
1:30 AM
A
Tap A can fill a tank in 10hrs,Tap B can fill it in 20hrs, and an out   [#permalink] 30 Nov 2017, 22:49
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