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

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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

The OA is A.

Is there someone who can help me here? It's a difficult question. <i class="em em-confused"></i>

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by DavidG@VeritasPrep » Thu Mar 15, 2018 5:54 am
VJesus12 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

The OA is A.

Is there someone who can help me here? It's a difficult question. <i class="em em-confused"></i>
If the tank is 1/4 full, we want to know how long it will take to fill 3/4 of the tank.

Rate for A = 1 tank in 10 hours, or 1/10
Rate for B = 1 tank in 20 Horus or 1/20
Rate for C (emptying the tank, so will be negative)= - 1 tank in 30 hours or -1/30

So let's see what would happen over the course of 3 hours. 1/10 + 1/20 - 1/30 = 6/60 + 3/60 - 2/60 = 7/60. So every three hours, the tank will be an additional 7/60 full.
Now let's see how many 3-hour intervals would elapse before the tank is 3/4 full. (Note: Obviously, the last interval need not be exactly 3 hours, so we'll be prepared to estimate/backtrack.)
Call 'x' the number of 3-hour intervals that elapse.
(7/60)x = 3/4

x = 3*60/(7*4) = 3*15/7 = 45/7 = 6 3/7.
Getting a ballpark is good enough. We're talking a little over 6 three-hour intervals. Six 3-hour intervals is 18 hours.
18 hours after 7 am would be 1 am the next day. We're going to overflow a little after that. Only A makes sense.
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by Vincen » Thu Mar 15, 2018 7:04 am
Hi Vjesus12.

Let's suppose that the capacity of the tank is 600 units.

The rates for each tap are:
- Tap A is 600 units in 10hr, hence the rate is 60 units/hr.
- Tap B is 600 units in 20hr, hence the rate is 30 units/hr.
- Tap C empties 600 units in 30hr, hence the rate is 20 units/hr.

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

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.

Therefore we have:
7:00 AM ---------150 units
10:00 AM--------220 units
1:00 PM ---------290 units
4:00 PM ---------360 units
7:00 PM ---------430 units
10:00 PM -------500 units
1:00 AM -------- 570 units

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.

This is why the correct option is A.

I hope it helps.

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hi

by Scott@TargetTestPrep » Sun Jun 02, 2019 4:20 pm
VJesus12 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
We can see that if taps A, B and C each work 1 hour consecutively in that order, then 1/10 + 1/20 - 1/30 = 6/60 + 3/60 - 2/60 = 7/60 of the tank would be filled. Since the tank is already 1/4 full, then the taps need to fill the remaining 3/4 of the tank. Since (3/4)/(7/60) = 3/4 x 60/7 = 45/7, it would appear that it will take 45/7 x 3 = 135/7 hours, or 19 2/7 hours, to fill the tank. However, remember that the problem asks for the time the tank will begin to overflow. That is, at certain point, if the tank is filled to its capacity by either tap A or B, then there won't be a tap C emptying it.

So let's see what happen after 18 hours (notice that, at this time, tap C just finishes emptying the pool and tap A takes over the filling):

1/4 + 6 x 7/60 = 1/4 + 7/10 = 15/60 + 42/60 = 57/60 = 19/20

We see that the leftover portion of the tank is 1/20, and it will take tap A (1/20)/(1/10) = 1/2 hour to fill the tank to its full capacity. Therefore, it will take 18 and ½ hours to fill the tank before it overflows.

7 AM + 18:30 hours = 25:30 --->25:30 - 24 = 1:30 AM the next day

Alternate Solution:

Let's assume that the tank has a capacity of 60 gallons. Since it takes 10 and 20 hours for A and B to fill the tank, respectively; the rate of A and B are 6 gal/hr and 3 gal/hr, respectively. Similarly, since it takes C 30 hours to empty the tank, the rate of C is 2 gal/hr.

Since 1/4 of the tank is full, there are 60/4 = 15 gallons of water in the tank and thus 60 - 15 = 45 gallons more should be filled before the tank overflows.

In a three hour period, 6 + 3 - 2 = 7 gallons of water accumulates in the tank. After six such cycles (or, after 18 hours), 6 x 7 = 42 gallons of water is in the tank and 45 - 42 = 3 more gallons is needed for the tank to overflow. Since it is tap A's turn to operate, it will take tap A 3/6 = 1/2 hours to fill 3 gallons; therefore the tank will overflow after 18.5 hours of operation.

7 AM + 18:30 hours = 25:30 ---> 25:30 - 24 = 1:30 AM the next day

Answer: 1/A

Scott Woodbury-Stewart
Founder and CEO
scott@targettestprep.com

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