Overflow?

Using the fact given that 1st and 2nd pipe fill the tank in 10 and 20 minutes individually, we can find that in one minute,1st pipe can fill in (4000/10)=400 liter water while 2nd pipe can fill in (4000/20)=200 liter water respectively.While the 3rd pipe can empty the tank in 5 minutes, 3rd pipe can empty out (4000/5)=800 liter water.

Note that 1st and 2nd pipe was opened together at 10 am and the 3rd pipe was opened after 7 minutes. During the 7 minutes before the 3rd pipe was opened, the water tank should be full because 1st and 2nd pipe can fill in (400+200) * 7=4200 liter water which is more than enough to fill in the water tank of 4000 liter capacity.

After 7 minutes which the time is 10.07 am, the water starts to decrease by the rate 200 liter every second (When the 1st and 2nd pipe fill in 400+200=600 liter water every second, the 3rd pipe empty out 800 liter, Hence the water decreases because 600-800= -200)

The duration between 10.07 am and 10.26 am is 26-7=19 minutes.Thus 4000-19 * 200=4000-3800=200 liter water

When the tank first starts being filled the 1st and 2nd pipe fill at 10 and 20 minutes individually. That means that every minte, the first pipe fills $\frac{1}{10}$ of the capacity and the second pipe fills $\frac{1}{20}$ of the capacity. That together is $\frac{3}{20}$ . Now practically after 7 minutes it should be overflowing, but we can't go above the maximum capacity. When the emptying pipe comes on it is empties 1/5 per minute so we need to subtract that giving us $\frac{-1}{20}$ . So after 19 minutes you lose -19/20. So that leaves you with 1/20 which is 200 liters.

at 10:07 am water tank will be full of it's capacity (4000 L).

4000 + (19x600) - (19x800)= 200 L.

Water 1st pipe can fill per minute= 4000/10= 400 L. Water 2nd pipe can fill per minute= 4000/20= 200 L. So, together in 7 minutes they can fill= (400 + 200) X 7= 4200 L. So in 7 minutes the full tank upto 4000 L will be filled.

Now, the 3rd pipe can empty per minute= 4000/5= 800 L. Hence, together the three pipes in 1 minute= (400 + 200 - 800) = -200 L i.e. empty 200 L. So, in 19 minutes, water emptied= 200 X 19 = 3800 L.

Therefore, water in the tank at 10:26 am= 4000 - 3800 = 200 L.

The first pipe fills in water at a rate of $\dfrac{4000}{10} = 400$ litres per minute.

The second pipe fills in water at a rate of $\dfrac{4000}{20} = 200$ litres a minute.

The third pipe empties the water at a rate of $\dfrac{4000}{5} = 800$ litres a minute.

By the $7^{\text{th}}$ minute, the first two tanks fill in $400 + 200$ litres per minute , so that's $600 \times 7 = 4200$ litres. But the capacity is only $4000$ litres, and thus the tank is filled completely.

From the $8^{\text{th}}$ minute till the $26^{\text{th}}$ minute, there is a net outflow of $200$ litres per minute ( $800 - 600$ ) There are a total of $19$ minutes where there is a net outflow of $200$ litres.

Thus the tank will have $4000 - \left( 200 \times 19 \right) = \boxed{200}$ litres.

>> To know how long take to 1st and 2nd pipe fill the tank: $\frac{1}{10}+\frac{1}{20} = \frac{1}{x} , x = \frac{20}{3}$ , therefore, at 10:07am the tank was already full.

>> To know the loss of water called by " $L$ ": $L = \frac{1}{10}+\frac{1}{20}-\frac{1}{5} , L = \frac{-1}{20}$

>> So, for each minute the water loss is $\frac{-1}{20}$ , that is equivalent to $200$ liters.

>> If the 3 pipes worked together for 19 minutes (from 10:07am to 10:26am), he lost $\beta$ liters.

>> $\frac{200 liters}{1min}=\frac{ \beta liters}{19 min}, \beta = 3800 liters$ .

>> Thus, the tank will have $4000 - 3800 = \boxed{200}$ liters at 10:26am.

pipe 1 +pipe 2 together can fill 1/10 + 1/20 of tank in a minute.i.e.,400+200 =600 l/m .after 7 minutes the tank overflows .the 3 pipes together can empty (1/10 +1/20 -1/5 ) part of tank.that is -1/20=200 l. in 19 minutes 3800 l.the remained water =200l

we note thatthe pipe was started to open at 10.00 till10.26 so the duration is about 27 minute

The amount of water entered the container is about 27*600=16200

the amount of water going out of the container is about 20*800=16000

so we subtract both answer and we got 200

Capacity of the first pump1 P1 = 4000/10 = 400 lit/min

Capacity of the second pump P2 = 4000/20 =200 lit/min

Capacity of the third Pump P3 = 4000/5 = 800 lit/min

After 7 min the flow from both pump1 and pump2 = (400(7) )+ (200(7)) = 4200lit

As the capacity of the tank is 4000 lit , 200 lit of water is overflown. So from 10.07 am there will be 4000 lit of water in the tank.

Now P1 and P2 will fill the tank and P3 will empty the tank.

(400 26 + 200 26)- (800*19)-200= 200 lit.

the tricky part is that 4200 liters are filled in 7 minutes but the capacity is 4000 liters. For the next 19 minutes, total water drained out-total water filled =800x19-(400+200)x19=3800 liters drained out. Hence the net water is 4000-3800=200 liters!

Pipe #1 = 400 L/min Pipe #2 = 200 L/min Pipe #3 = -800 L/min

Since Pipe #1 and Pipe #2 were opened at the same time, they have a total rate of 600 L/min. After 7 min then poured out 4200 L of water which overflows so the water level stays at 4000 L. After Pipe #3 is opened, water is pouring out at -200 L/min total.(draining duh!) Since 26 mins - 7 mins = 19 mins. Pipe #3 has been draining water for 19 min, amassing a total of -3800 L. 4000 L - 3800 L = $\boxed{200}$

We need to consider capacity & overflow in perspective in order to arrive at solution. Calculate discharge capacity of each pipes in terms of liters per minute. Pipe One - P1-Discharge capacity = 4000lits/10mins = 400lpm Pipe Two- P2-Discharge Capacity= 4000lits/20mins = 200lpm Pipe Three-P3-Discharge Capicity =4000lits/5mins = 800lpm

Lets Calculate the amount of water in-flow during first seven minutes after 10:00 Hrs P1- 400lpm x 7mins = 2800 lits P2-200lpm x 7mins = 1400 lits

Total Inflow during forst seven minutes = 2800 + 1400 = 4200 lits but as the installed capicity is only 4000 lit the additional 200 lit shall overflow. So the Tank is full after elapse of first seven minutes

Now let see what happens after elapse of first 7 minutes till 10:26 hrs ie during 19 minutes P1- 400lit x 19 mins = 7600 lits P2 - 200lits x 19 mins =3800 lits

Total Inflow in 19 minutes = 7600 + 3800 = 11400 lits Total inflow since 10 AM = 11400lis + 4000lits = 15400 lits

Lets see the out flow during 19 minutes from P3

P3- 800lit x 19 = 15200lits ie this much water has out flowed

Hence Total quantity remained in the Tank= Total inflow - Total Out flow= 15400- 15200= 200 lits

In one min pipe 1 fill 400 lt and pipe 2 fill 200 lt .at 10:07 am they full the tank.And pipe 3 is withdrawing water at the rate of 800 lt/min.in 19 min pipe 3 will extract 3800 lt of water.so 200 lt left.

(20/3):(7) = 4000/x ---> 20/21 = 4000/x ----> x = 4200. So, x - 4000 = 4200 - 4000 = 200. Answer : 200

1 tubo = 400 l/m ; 2 tubo = 200 l/m; => enchem.

3 tubo = 800 l/m.

o exercício diz que o 1 e o 2 estavam juntos,logo => 400 + 200 = 600 l/m. com 7 minutos,eles encheram o tanque.(4000 l).

E o 3 foi acionado (800 l).800-600 = 200 l esvaziados / minuto., no instante 26 => 26-7 = 19. => 19.200 = 3800 => 4000 - 3800 = 200 l ;