Pipes and Cistern
- The volume of water flowing through a pipe is directly proportional to square of it’s radius. A tank has four inlet pipes with diameters as 2 cm, 4 cm, 6 cm and 8 cm. If the smallest pipe, alone, can fill a tank in 30 hours, then how much time would all the four pipes, when working together would take?
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We are given that V = k (r)²
where V is volume of water and ‘r’ is radius of pipe and K is a constant.The smallest pipe takes 30 hours to fill the tank alone, hence work done in 1 hour = 1 30 radius = diameter = 2 = 1 2 2 1 = k( 1 )² so, k = 1 30 30 Work done in 1 hour by Pipe 2 = 1 
4 
² = 4 30 2 30 Work done in 1 hour by Pipe 3 = 1 6 ² = 9 30 2 30 Work done in 1 hour by Pipe 4 = 1 8 ² = 16 30 2 30
Correct Option: A
We are given that V = k (r)²
where V is volume of water and ‘r’ is radius of pipe and K is a constant.The smallest pipe takes 30 hours to fill the tank alone, hence work done in 1 hour = 1 30 radius = diameter = 2 = 1 2 2 1 = k( 1 )² so, k = 1 30 30 Work done in 1 hour by Pipe 2 = 1 4 ² = 4 30 2 30 Work done in 1 hour by Pipe 3 = 1 6 ² = 9 30 2 30 Work done in 1 hour by Pipe 4 = 1 8 ² = 16 30 2 30 In 1 hour, work done by all 4 pipes = 1 + 4 + 9 + 16 = 30 = 1 30 30 30 30 30
Hence, the whole tank gets filled in 1 hour.
- Two pipes can fill a tank in 10 minutes and 30 minutes respectively and a third pipe can empty the full tank in 20 minutes. If all the three pipes are opened simultaneously, the tank will be filled in
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On the basis of above given question ,
Part of the tank filled in 1 minute by pipe 1 = 1 10 Part of the tank filled in 1 minute by pipe 2 = 1 30 Part of the tank filled in 1 minute by pipe 3 = - 1 20
When all the three pipes are opened simultaneously,
Correct Option: D
On the basis of above given question ,
Part of the tank filled in 1 minute by pipe 1 = 1 10 Part of the tank filled in 1 minute by pipe 2 = 1 30 Part of the tank filled in 1 minute by pipe 3 = - 1 20
When all the three pipes are opened simultaneously,Part of the tank filled in 1 minute = 1 + 1 - 1 = 6 + 2 - 3 = 5 = 1 10 30 20 60 60 12
Hence, the tank will be filled in 12 minutes.
- A cistern can be filled by two pipes in 20 and 30 minutes respectively. Both pipes being opened, when must the first pipe be turned off so that the cistern may be filled in 10 minutes more?
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As per the given in question ,
In 1 minute both pipes can fill = 1 + 1 part of the cistern 20 30 In 10 minutes, second pipe can fill = 1 × 10 = 1 part 30 3 Cistern filled by both pipes = 1 - 1 = 2 3 3
Correct Option: D
As per the given in question ,
In 1 minute both pipes can fill = 1 + 1 part of the cistern 20 30 In 10 minutes, second pipe can fill = 1 × 10 = 1 part 30 3 Cistern filled by both pipes = 1 - 1 = 2 3 3 ∴ Time taken by both the pipes to fill 2/3 part of cistern = 12 × 2 = 8 minutes 3
Therefore, the first pipe can be turned off after 8 minutes.
- Tap A, B and C are connected to a water tank and the rate of flow of water is 42 litres/hr, 56 litres/ hr and 48 litres/hr respectively. Tap A andB fill the tank while tap C empties the tank. If all the three taps are opened simultaneously, the tank gets completely filled up in 16 hours. What is the capacity of the tank?
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From the question ,
When all three taps are opened simultaneously, Net amount of water filled in the tank in 1 hour = 42 + 56 – 48 litres = 50 litres
The tank gets completely filled in 16 hours.
∴ Capacity of the tank = Net amount of water × TimeCorrect Option: D
From the question ,
When all three taps are opened simultaneously, Net amount of water filled in the tank in 1 hour = 42 + 56 – 48 litres = 50 litres
The tank gets completely filled in 16 hours.
∴ Capacity of the tank = Net amount of water × Time
∴ Capacity of the tank = 16 × 50 = 800 litres
- Two full tanks, one shaped like a cylinder and the other like a cone, contain jet fuel. The cylindrical tank holds 500 L more than the conical tank. After 200 L of fuel has been pumped out from each tank, the cylindrical tank contains twice the amount of fuel in the conical tank. How many litres of fuel did the cylindrical tank have when it was full?
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Let conical tank contain ‘q’ litres of fuel, then cylindrical tank would hold (q + 500) litres.
So, (q – 200)2 = q + 500 – 200
⇒ 2q – 400 = q + 300
⇒ 2q - q = 400 + 300
⇒ q = 700Correct Option: D
Let conical tank contain ‘q’ litres of fuel, then cylindrical tank would hold (q + 500) litres.
So, (q – 200)2 = q + 500 – 200
⇒ 2q – 400 = q + 300
⇒ 2q - q = 400 + 300
⇒ q = 700
Hence, cylindrical tank would hold 700 + 500 = 1200 L
