A 500-litre water storage tank is situated at the top of a building at a height of 300 feet.The tank,which is completely full,has two outlet pipes and one inlet pipe.Veeru climbs up to the tank and opens an outlet which can empty a full tank in 10 minutes. At the same time jay opens an inlet pipe which can fill an empty tank in 12 minutes. 1)In how much time will the tank be empty? 2)when the tank becomes half empty,veeru opens the other outlet pipe which can empty a full tank in 15 minutes.In how much time(from the start)will the tank be empty? 3)After 10 minute veeru closes the 1st outlet pipe and opens the 2nd one the tank then empties in another 10 minutes.In how much time can the 2nd outlet pipe empty an open tank?

60min

1 hour

1) Well, with Veeru emptying the tank in 10 minutes and Jay filling it in 12 minutes, it's like a battle between drain and gain. And in this case, the drain wins! So, the tank will be empty in 10 minutes.

2) Ah, the tank is now half empty and Veeru decides it's time to bring out the big guns. With the second outlet pipe taking 15 minutes to empty a full tank, it's like a race against time! But don't worry, I'm sure Jay's feeling the pressure. In this case, the tank will be empty in 15 minutes.
3) After 10 minutes, Veeru realizes the first outlet pipe was just too good at its job and decides to close it. Good call, Veeru! Now, with only the second outlet pipe in action, the tank empties in another 10 minutes. So it seems like the second outlet pipe can empty an open tank in 10 minutes.

1) To find the time in which the tank will be empty, we need to determine the rate at which water is being filled and emptied.

Let's calculate the rate at which water is being emptied by Veeru's outlet pipe:
Veeru's outlet pipe can empty a full tank in 10 minutes, so its emptying rate is 1 tank / 10 minutes, which can also be expressed as 1/10 tanks per minute.

The tank has a capacity of 500 liters, so the water flow rate is 500 liters / 10 minutes, which is equal to 50 liters per minute (since 1 tank = 500 liters).

Next, let's calculate the rate at which water is being filled by Jay's inlet pipe:
Jay's inlet pipe can fill an empty tank in 12 minutes, so its filling rate is 1 tank / 12 minutes or 1/12 tanks per minute.
Again, this can also be expressed as 500 liters / 12 minutes or approximately 41.67 liters per minute.

Now, we can determine the net rate of water flowing out of the tank:
Net rate = inlet pipe rate - outlet pipe rate
Net rate = 41.67 - 50
Net rate = -8.33 liters per minute

Since the net rate is negative (-8.33 liters per minute), the tank is being emptied.

To calculate the time it takes for the tank to be empty, we can divide the initial quantity (500 liters) by the net rate:
Time = Initial quantity / Net rate
Time = 500 liters / (-8.33 liters per minute)
Time ≈ 60 minutes

Therefore, it will take approximately 60 minutes for the tank to be empty.

2) When the tank becomes half empty, Veeru opens the other outlet pipe, which can empty a full tank in 15 minutes. Let's calculate the new net rate.

Since half the tank is empty, the remaining water level is 250 liters.

The rate at which water is being emptied by the new outlet pipe is 1 tank / 15 minutes or 500 liters / 15 minutes, which is approximately 33.33 liters per minute.

Now we need to calculate the new net rate when the tank is half empty:
Net rate = inlet pipe rate - outlet pipe rate
Net rate = 41.67 - 33.33
Net rate = 8.34 liters per minute

Since the net rate is positive (8.34 liters per minute), the tank is being filled now.

To calculate the time it takes for the tank to be empty from this point onwards, we can divide the remaining quantity (250 liters) by the net rate:
Time = Remaining quantity / Net rate
Time = 250 liters / 8.34 liters per minute
Time ≈ 30 minutes

Therefore, it will take approximately 30 minutes from the point the tank becomes half empty for the tank to be completely empty.

3) After 10 minutes, Veeru closes the first outlet pipe and opens the second one. The tank then empties in another 10 minutes.

Let's calculate the net rate of the second outlet pipe:

Since the tank empties in 10 minutes, the rate at which water is being emptied by the second outlet pipe is 1 tank / 10 minutes. This is equivalent to 500 liters / 10 minutes or 50 liters per minute.

Hence, the second outlet pipe can empty a full tank at a rate of 50 liters per minute.

Therefore, the second outlet pipe alone can empty an open tank in 10 minutes.

To answer these questions, we need to determine the flow rates of the inlet and outlet pipes.

Let's start by calculating the flow rate of the inlet pipe:
The inlet pipe can fill the tank in 12 minutes, so it fills 1/12th of the tank in 1 minute.

Next, let's calculate the flow rate of the first outlet pipe:
The first outlet pipe can empty a full tank in 10 minutes, so it empties 1/10th of the tank in 1 minute.

Now, let's move on to the first question:

1) In how much time will the tank be empty?

Since the inlet pipe is filling the tank and the first outlet pipe is emptying it, we need to find the net flow rate. The net flow rate is the difference between the flow rates of the inlet and outlet pipes.

Net flow rate = Inlet flow rate - Outlet flow rate

Net flow rate = 1/12 - 1/10 = (5 - 6) / 60 = -1/60

As the net flow rate is negative (-1/60), this means the tank is emptying.

To determine the time it takes for the tank to be completely empty, we can use the equation:

Time = Tank capacity / Net flow rate

Given that the tank capacity is 500 liters, which is equal to 500/1000 = 0.5 cubic meters:

Time = 0.5 / (-1/60) = 0.5 * (-60) = -30 minutes

Since we cannot have a negative time, we can conclude that the tank will never be completely empty.

Moving on to the second question:

2) When the tank becomes half empty, Veeru opens the second outlet pipe, which can empty a full tank in 15 minutes. In how much time (from the start) will the tank be empty?

When the tank becomes half empty, it means it has a volume of 0.5 * 500 liters = 250 liters.

Now, we have two outlet pipes working together, so we need to add their flow rates to get the net outlet flow rate.

Flow rate of the second outlet = 1/15

Net outlet flow rate = 1/10 + 1/15

To find the time it takes for the tank to be completely empty:

Time = Tank capacity / (Net flow rate - Inlet flow rate)

Time = 0.5 / (1/10 + 1/15 - 1/12)

Simplifying,

Time = 0.5 / (3/30 + 2/30 - 5/60)
= 0.5 / (5/30)
= 3 minutes

So, from the start, it will take 3 minutes for the tank to be completely empty after opening the second outlet when the tank becomes half empty.

Finally, let's answer the third question:

3) After 10 minutes, Veeru closes the first outlet pipe and opens the second one; the tank then empties in another 10 minutes. In how much time can the second outlet pipe empty an open tank?

Since the second outlet pipe can empty a full tank in 15 minutes, we can assume it has a flow rate of 1/15.

Given that the tank empties in another 10 minutes after Veeru opens the second outlet pipe, the net flow rate is the same as the flow rate of the second outlet pipe, which is 1/15.

To find the time it takes for the second outlet pipe to empty an open tank:

Time = Tank capacity / Net flow rate

Time = 0.5 / (1/15)

Simplifying,

Time = 0.5 * (15/1)
= 7.5 minutes

So, it will take 7.5 minutes for the second outlet pipe to empty an open tank.