Pipes and Cistern

Two pipes can fill a tank in $8 \mathrm{h}$ and $12 \mathrm{h}$ respectively whereas an escape pipe can empty it in $6 \mathrm{h}$. If the three pipes are opened at $1$ PM, $2$ PM and $3$ PM respectively, at what time will the tank be filled?

Three taps are fitted in a cistern. The empty cistern is filled by the first and the second taps in $3$ h and $4$ h respectively. The full cistern is emptied by the third tap in $5$ h. If all three taps are opened simultaneously, then the empty cistern will be filled up in.

Which of the following statements are necessary to answer the question:

A tank is fitted with two taps A and B. In how much time will the tank be full if both the taps are opened together ?
(i) A is $50$% more efficient than B
(ii) A alone takes $16$ hours to fill the tank
(iii) B alone takes $24$ hours to fill the tank.

A water filling Pipe $P$ is $5 \mathrm{times}$ faster than second Pipe $Q$. If $P$ fills a cistern in $30 \mathrm{minutes}$. How long will it take to fill the tank, when both the pipes are kept in operation simultaneous?

A swimming pool has $3$ drain pipes. The first two pipes A and B, operating simultaneously, that of taken by C alone. Pipe A, working alone, takes half the time taken by pipe B. Together they take $6$ hrs $40$ minutes to empty the pool. Time taken by pipe A to empty the pool, in hours, is

Ajit is ranked seventh from the top and twenty fifth from the bottom in a class. How many students are there in that class?

Six pipes are fitted to a water tank. Some of these are filling pipes, others are emptying pipes. Each filling pipes can fill the tank in 9 hrs and each waste pipe can empty the tank in$6 \mathrm{hrs}$. On opening all the pipes in the empty tank is filled in $9 \mathrm{hrs}$. Find the number of filling pipes?

A Cistern is filled by pipe A in 8 hrs and the full Cistern can be leaked out by an exhaust pipe B in 12 hrs. If both the pipes are opened in what time the Cistern is full?

A boat covers $12 \mathrm{km}$ upstream and$18 \mathrm{km}$downstream in $3 \mathrm{hrs}$, while it covers$36 \mathrm{km}$upstream and $24 \mathrm{km}$downstream in $6\frac{1}{2} \mathrm{hours}$. What is the speed of the current?

There are two water taps in a tank that can fill the empty tank in $12 \mathrm{hours}$ and $18 \mathrm{hours}$ respectively. It is seen that there is a leakage point at the bottom of the tank which can empty the completely filled tank in $36 \mathrm{hours}$. If both the water taps are opened at the same time to fill the empty tank and the leakage point was repaired after $1 \mathrm{hour}$, then in how much time the empty tank will be completely filled?

There are three inlet taps whose diameters are $1 \mathrm{cm}$, $2 \mathrm{cm}$, and $3 \mathrm{cm}$, respectively. Rate of flow of water is directly proportional to the square of the diameter. It takes $9$ min for the smallest pipe to fill an empty tank. Find the time taken to fill an empty tank when all the three taps are opened.

A swimming pool can be filled by pipe $\mathrm{A}$ in $3 \mathrm{h}$ and by pipe $\mathrm{B}$in $6 \mathrm{h}$, each pump working on its own. At $9$am, pump $\mathrm{A}$ is started. At what time will the swimming pool be filled if pump $\mathrm{B}$ is started at $10\mathrm{am}$ ?

It takes $6 \mathrm{h}$ for pump $\mathrm{A}$, used alone, to fill a tank of water. Pump $\mathrm{B}$used alone takes $8$h to fill the same tank.$\mathrm{A}, \mathrm{B},$ and another pump $\mathrm{C}$all together fill the $tank$ in $2 \mathrm{h}$. How long would pump $\mathrm{C}$ take, used alone, to fill the tank?

The discharge of pipe A is $200 \mathrm{liters}$ per hour and that of pipe B is $300 \mathrm{liters}$ per hour while that of pipe C is $250 \mathrm{liters}$ per hour. A and B are used to fill the tank while C is used to empty the tank. If B and C are open alternately with pipe A, then find the time required to fill a tank of capacity $4500 \mathrm{litres}$.

Two pipes A and B, Pipe A can fill the tank in $250 \min$, it is operational for $50 \min$, Pipe B is also opened along with pipe B and fill the remaining tank in $150 \min$. Find the time taken by pipe B alone to fill the tank.

The time taken by pipe A to fill the tank is $1 \mathrm{hour}$, the time is taken by pipe B to fill the tank is $2 \mathrm{hours}$ and the time is taken by pipe C to empty the tank is $1.5 \mathrm{hours}$. Pipe A and pipe B is opened together for $4 \mathrm{hours}$ and then pipe C is opened. Find the time taken by pipe C to empty the tank.

Jaya and Sachin use a straw to drink juice from the same vessel. Jaya alone takes $2 \mathrm{minutes}$ to drink $20 \mathrm{ml}$ of the juice and Sachin alone takes $1 \mathrm{minute}$ to drink $20 \mathrm{ml}$of juice. They drink together and empty a full vessel in $2 \mathrm{minutes}$. After the vessel gets empty, a refilling straw that can fill $400 \mathrm{ml}$ in $8$ $\mathrm{minutes}$ is also put in the vessel. In how much time will the container be full if all the straws are simultaneously used?

Pipe A can fill a tank in $20 \min .$ and Pipe B can empty a tank in $30 \min .$. In how many minute the tank will be filled when both pipes are opened? 

Pipes $A$, $B$ and $C$ can fill a tank in $15, 30$ and $40 \mathrm{hours}$, respectively. Pipes $A, B$ and $C$ are opened at $6 \mathrm{A}.\mathrm{M}., 8 \mathrm{A}.\mathrm{M}.,$ and $10 \mathrm{A}.\mathrm{M}.,$ respectively, on the same day. When will the tank be full?

Pipe A and B can empty a full tank in $18 \mathrm{hours} \mathrm{and} 24 \mathrm{hours}$, respectively. Pipe C alone can fill the tank in $36 \mathrm{hours}$. If the tank is $\frac{5}{6}$ full and all the three pipes are opened together, then in how many hours will the tank be emptied?