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

Question

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

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

Source:Experts' Global

pushpitkc · Answer

Assume capacity of the tank is 600 units.

The rate of filling the taps 
Tap A is 60 units/hr
Tap B is 30 units/hr
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)

MvArrow · Answer

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

lichting · Answer

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!

EgmatQuantExpert · Answer

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

gracie · Answer

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

KanishkM · Answer

let total volume be 60 ml , then A will fill in 6 units, B will fill in 3 units and C will empty by 2 units

We begin at 7AM, and will taps will work in the order A, B and C, 12 ml is already full remaining 48 needs to be filled

in 3 hrs from 7 - 10, Net change will be of 7 units 
in 3 hrs it will be 41, 34, 27,20,13

so after 13:30 hrs it will begin to over fall

A

ScottTargetTestPrep · Answer

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

Archit3110 · Answer

rate of A ; 1/10 
rate of B ; 1/20
rate of C ; 1/30
let tank be 60
so time of a ; 6 per hrs b. 3 per hrs c . 2 per hrs
combined work for 3 hrs ; 6+3-2 ; 7 per hour 
given that tank is 1/4th full so we need to fill ; 3/4*60 ; 45 ltrs
45 ltrs can be filled in ; 45/7 ; 6 units + 3 units for A ; 
1 unit ; 3 hrs ; 6*3 ; 18 hrs + 3/6 ; 1/2 hrs ; 18.5 hrs 
total time ; 7am+ 18.5 hrs ; 1;30 am 
IMO A

Panda2046 · Answer

Let capacity of tank be 600l
A fills 60 units in an hour, B 30 units and C can empty 20 units
In 3 hours tank will fill 70 units 
At 7 am tank has 150l of water and we need to fill 450l
In 18 hours we can fill 420 l
And then A will fill the remaining 30l in half hour
So 1.30am next day it will overflow

Posted from my mobile device

vg3184 · Answer

this stem is flawed.. how do we know, Its tap A that will turn on right at 7 am....

we should also be given is the stem that tap c just finished off its one hour turn, right at 7 am

bumpbot · Answer

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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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