Pipes and Cisterns Questions - 1

Two pipes A and B can a cistern in 20 minutes and 25 minutes respectively. Both are opened together, but after 5 minutes, B is turned off. Then how much longer will the cistern take to fill ?
• 8 Minutes
• 20 Minutes
• 15 Minutes
• 10 Minutes
• 11 Minutes
Explanation

Cistern filled by A and B in 5 ninutes.

= 5 $\displaystyle \left(\frac{1}{20} + \frac{1}{25}\right) = \frac{9}{20}$

Part unfilled = $\displaystyle \left(1 - \frac{9}{20}\right) = \frac{11}{20}$

Now $\displaystyle \frac{1}{20}$ part is filled by A in 1 minute.

$\displaystyle \frac{11}{20}$ part wiil be filled by A in 20% of $\displaystyle \frac{11}{20}$ = 11 minutes.

Workspace
A pipe can fill a cistern in 12 minutes and another pipe in 15 minutes, but a third pipe can empty it in 6 minutes. The first two pipes are kept open for 5 minutes in the beginning and then the third pipe is also opened. In what time is the cistern emptied ?
• 50 minutes
• 30 minutes
• 35 minutes
• 45 minutes
• 40 minutes
Explanation

Cistern filled in 5 ninutes.

= 5 $\displaystyle \left(\frac{1}{12} + \frac{1}{15}\right) = \frac{3}{4}$ of tank.

After 5 minutes, let the third pipe emptied be "t" minutes, then = t $\displaystyle \left(\frac{1}{12} + \frac{1}{15}\right) + \frac{3}{4} = \frac{t}{6}$

t = 45 minutes.

Workspace
Two pipes A and B can fill a tank in 15 hours and 20 hours respectively while a third pipe â€œCâ€ can empty the full tank in 25 hours, all the three pipes are open in the beginning. After 10 hours â€œCâ€ is closed. Then find in how much time tank be full ?
• 1 hour
• 2 hours
• 3 hours
• 4 hours
• 12 hours
Explanation

Water tank filled in 10 hours.

= 10 $\displaystyle \left(\frac{1}{15} + \frac{1}{20} - \frac{1}{25}\right) = \frac{23}{30}$

Remaining part = 1 - $\displaystyle \frac{23}{30} = \frac{7}{30}$

Now work done by (A + B) in 1 hour = $\displaystyle \left(\frac{1}{15} + \frac{1}{20}\right) = \frac{7}{60}$

It means $\displaystyle \frac{7}{60}$ part is filled in 1 hour.

So, $\displaystyle \frac{7}{30}$ part is filled in = $\displaystyle \frac{60}{7} \times \frac{7}{30}$ = 2 hours.

Workspace
Two pipes A and B can separately fill a cistern in 7$\displaystyle \frac{1}{2}$ minutes and 5 minutes respectively and a waste pipe â€œCâ€ can carry off 14 litres per minute. If all the pipes are opened when the cistern is full, it is emptied in 1 hour. How many litres does it hold (the tank capacity) ?
• 40 litres
• 30 litres
• 20 litres
• 50 litres
• 80 litres
Explanation

Cistern filled by (A + B) in 1 minute.

= $\displaystyle \frac{2}{15} + \frac{1}{5} = \frac{1}{3}$

Let the capacity of tank be "Z" litres.

In one hour, Inlet in litres + Z litres = outlet in litres.

= 60 $\displaystyle \times \frac{\text{Z}}{3}$ + Z = 14 x 60 = Z = 40.

Hence, the capacity of cistern = 40 litres.

Workspace
A cistern has a leak which would empty it in 6 hours. A tap is turned on, which admits 4 litres a minute into the cistern and is now emptied in 8 hours. What is the capacity of the cistern?
• 5500 litres
• 4500 litres
• 5760 litres
• 6350 litres
• 5700 litres
Workspace
Two pipes A and B can fill a cistern in 24 minutes and 32 minutes respectively. Both the pipes being opened, find when the second pipe must be turned off so that the cistern may be just full in 18 minutes ?
• 6 minutes
• 12 minutes
• 20 minutes
• 8 minutes
• 30 minutes
Explanation

Let the second pipe be turned of after "t" minutes.

Then, work done by (A + B) in x minutes is => t $\displaystyle \left(\frac{1}{24} + \frac{1}{32}\right) = \frac{7\text{t}}{92} => \left(1\right)$

Also, work done by A in (18-t) minutes = $\displaystyle \frac{18-\text{t}}{24} => \left(2\right)$

Now (1) + (2) => $\displaystyle \frac{7\text{t}}{96} + \frac{18-\text{x}}{24}$ = 1.

t = 8.

Workspace
A, B, C are pipes attached to a cistern. A and B can fill it in 20 minutes and 30 minutes respectively while C can empty it in 15 minutes. If A, B, C be kept open successfully for 1 minute each, how soon will the cistern be filled ?
• 160 minutes
• 157 minutes
• 167 minutes
• 150 minutes
• 180 minutes
Explanation

Work done in 3 minutes by 3 pipes.

Then, work done by (A + B) in x minutes is = $\displaystyle \frac{1}{20} + \frac{1}{30} - \frac{1}{15} = \frac{1}{60}$

It means $\displaystyle \frac{1}{60}$ of tank is filled in 3 minutes.

$\displaystyle \frac{55}{60}$ part of the cistern is filled in 3 x 55 or 165 minutes.

Out of remaining $\displaystyle \frac{5}{60}$ cistern, $\displaystyle \frac{1}{20}$ is filled by A in 1 minute, and remaining is

$\displaystyle \frac{5}{60} - \frac{1}{20}$ i.e. $\displaystyle \frac{1}{30}$ is filled by B in 1 minute.

Therefore answer is, 165 + 2 = 167 minutes.

Workspace
Two pipes P and Q can fill a cistern in 12 minutes and 16 minutes respectively. Both are opened together, but after 4 minutes Q is turned off. Then the cistern will be full in ?
• 20 minutes
• 12 minutes
• 15 minutes
• 10 minutes
• 5 minutes
Explanation

Work done by both in 4 minutes.

= 4 $\displaystyle \left(\frac{1}{12} + \frac{1}{16}\right) = \frac{7}{12}$

Remaining part of cistern = $\displaystyle \left(1 - \frac{7}{12}\right) = \frac{5}{12}$

Now $\displaystyle \frac{5}{12}$ part is filled by P in $\displaystyle \frac{5}{12} \times \frac{12}{1}$ = 5 minutes.

Workspace
Pipe can fill a cistern in 7 hours. Due to a leak in the bottom the cistern is just in 8 hours. The leak can empty the full cistern in ?
• 26 hours
• 56 hours
• 36 hours
• 46 hours
• 16 hours
Explanation

$\displaystyle \frac{1}{7}$ of tank water leak in 8 hours.

So, full tank leak in 7 x 8 = 56 hours.

Workspace
A cistern has a leak which would empty it in 8 hours. A tap is turned on which admits 6 ltrs a minute into the cistern and it is now emptied in 12 hours. How many ltrs does the cistern hold?
• 1880 ltrs
• 2880 ltrs
• 3880 ltrs
• 4880 ltrs
• 5880 ltrs
Workspace

Practice Test Report

Descriptions Status
Attempted Questions
Un-Attempted Questions

Pipes and Cisterns Formulas and Concepts

1. If pipe A can fill a tank in â€˜nâ€™ number of hours/min, then in 1 hour part of tank filled by A is $\displaystyle \frac{1}{\text{n}}$ part of the tank.

2. If, in one hour pipe A can fill $\displaystyle \frac{1}{\text{n}}$th part of the tank then, the tank completely filled in â€˜nâ€™ number of hours.

Note: Here â€˜nâ€™ denotes time; it can be hours/minutes.

3. If pipe A can fill a tank in â€˜xâ€™ hours while B can fill the same tank in â€˜yâ€™ hours. And Pipes A and B simultaneously can fill the tank in one hour = $\displaystyle \frac{\text{x} \ + \ \text{y}}{\text{x} \text{y}}$th part, then total work = $\displaystyle \frac{\text{x} \text{y}}{\text{x} \ + \ \text{y}}$ hours.

4. If pipes A and B working together can fill a work in â€˜xâ€™ hours, if A alone can fill the tank in â€˜yâ€™ hours, then B alone can fill the tank in = $\displaystyle \frac{1}{\text{x}} - \frac{1}{\text{y}} = \frac{\text{xy}}{\text{x} \ - \ \text{y}}$ hours.

5. If pipe A can fill a tank in x hours, pipe B can empty the full tank in y hours, If both the pipes are opened simultaneously, then the tank can be filled in = $\displaystyle \frac{1}{\text{x}} - \frac{1}{\text{y}} = \frac{\text{xy}}{\text{x} \ - \ \text{y}}$ hours.

Time: