On this page we have considered the following types of questions:-
So let us solve each type of problem on How To Solve Pipes and Cisterns Questions one by one to understand the concept more clearly and efficiently.
1.Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?
Options:
A. 12 min.
B. 15 min.
C. 25 min.
D. 50 min.
Solution:
Part filled by A in 1 minute = $= \frac{1}{20}$
Part filled by B in 1 minute $ = \frac{1}{30}$
Part filled by (A + B) in 1 minute $ = \frac{1}{20} + \frac{1}{30} = \frac{1}{12}$
∴ Both pipes can fill the tank in 12 minutes
Correct option: A
2.There are two pipe A and B connected to a tank. The tank can be filled in 6 minutes, if pipe A takes 5 minutes less than pipe B, How much time will pipe B take if it is alone filling the tank.
Options:
A. 15 min
B. 12 min
C. 10 min
D. 5 min
Solution:
Time taken by Pipe A to fill the tank = x minutes
Therefore, pipe B will fill the bucket in (x+5) minutes.
Now, when both the pipes are filling the tank = $\frac{1}{x}+ \frac{1}{x+5}= \frac{1}{6}$
On solving we get, x = 10
So, pipe A can fill in 10 minutes and pipe B can fill the bucket in (x+5)= 10+ 5 =15 mins.
Correct option: A
3.One pipe can fill a tank two times as fast as another pipe. If together the two pipes can fill the tank in 30 minutes, then the slower pipe alone will be able to fill the tank in:
Options:
A. 81 min.
B. 90 min.
C. 92 min.
D. 192 min.
Solution:
Let the slower pipe alone fill the tank in x minutes.
Then, faster pipe will fill it in $\frac{x}{3}$ minutes.
$\eqalign{ & \therefore \frac{1}{x} + \frac{2}{x} = \frac{1}{{30}} \cr & \Rightarrow \frac{3}{x} = \frac{1}{{30}} \cr & \Rightarrow x = 90\,\text{minutes} \cr} $
Correct Option: B
1.A pipe can fill a vessel with milk in two hours. But there was a leakage in the pipe which made it took $3$ hours to fill the vessel with milk. The leak can drain all the milk of the vessel in how much time?
Options:
A. 10 hrs
B. 3 hrs
C. 5 hrs
D. 13 hrs
Solution:
Due to leak the vessel filled in one hour$ = \frac{1}{2} – \frac{1}{3} = \frac{1}{3}$
It means leak will empty the vessel in 3 hrs.
Correct option: B
2.A cistern takes 5 hrs to be filled by pipe. But there is one leakage in the pipe due to which it takes 15 hrs. Find out how much time will the leakage pipe to empty the cistern?
Options:
A. 7 hrs
B. 6 hrs
C. 7.30 hrs
D. 7.30 min
Solution:
Cistern is filled in 5 hours,
Therefore in 1 hour part filled is = $\frac{1}{5}$
Now, due to leakage in pipe, filled part in $1 hour = 1/15$
Part of the cistern emptied, due to leakage in 1 hour $ = \frac{1}{5} – \frac{1}{15} = \frac{2}{15}$
Therefore the leak pipe will empty the cistern in $\frac{15}{2}$ = 7.30 hrs.
Correct option: C
1. Two taps T1 and T2 can fill a bucket in 15 minutes and 30 minutes. Both the taps are opened together. However, after 5 minutes, tap T1 is closed. What is the total time required to fill the bucket?
Options:
A. 22 min 30 sec
B. 20 min
C. 18 min and 40 sec
D. 16 min and 40 sec
Solution:
Part filled in 5 min = $5 * (\frac{1}{15}+ \frac{1}{30})= 5 * \frac{1}{10} = \frac{1}{2}$
Remaining part =$ (1-\frac{1}{2})= \frac{1}{2}$
To fill \frac{1}{2} T2 will take \farc{1}{2} \times 30 = 15 min.
Therefore, the bucket will be filled in = 5 + 15 = 20 min.
Correct option: B
2. A pond can be filled by two pipes P1 and P2. P1 takes 5 hours and P2 takes 10 hours. There is another pipe P3 attached to the pond which can empty the pond in 6 hours. If all the pipes are opened at the same time then in how much time will the empty pond be fully filled?
Options:
A. $\frac{10}{48} hrs$
B. 7.30 hrs
C. $\frac{7}{3} hrs$
D. $\frac{21}{3} hrs$
Solution:
Time taken by Pipe P1 to fill the tank = 5 hr
Time taken by pipe P2 to fill the tank = 10 hr
Time taken by pipe P3 to empty the tank = 6 hr
Therefore, pipe P1 and P2 fills $\frac{1}{5} $th and $\frac{1}{10}$ th part of the pond in 1 hour respectively.
Part of the pond emptied in 1 hour by pipe P3 = $\frac{1}{6}$
Therefore, in 1 hour part of the pond filled is = $(\frac{1}{5} + \frac{1}{10} – \frac{1}{6})$
$= \frac{2}{15}$
Therefore, tank will be filled completely in $\frac{15}{2} = 7.30 hrs.$ hrs
Correct option: B
3.Pipe A takes 12, pipe B takes 16, and Pipe C takes 20 hrs to fill a water container. Pipe A was opened first. After 2 hrs, pipe B was opened. After 2 hrs from the start of B, pipe C was also opened. Find the time when water container will be full after opening of pipe C?
Options:
A. $\frac{112}{34}$
B. $\frac{311}{14}$
C. $\frac{1234}{47}$
D. $\frac{321}{47}$
Solution:
Let water container get full in x hrs.
Then part filled by pipe A in x hrs + part filled by pipe B in (x-2) hrs + part filled by pipe C in (x-4) hrs = 1
$\frac{x}{12}+ \frac{x – 2 }{16}+ \frac{x – 4 }{20}= 1$
x = $ \frac{162}{47} = \frac{321}{47}$ hrs
Correct Option: D