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?

A box measures externally $210 \mathrm{cm}$ long, $60 \mathrm{cm}$ wide and $30 \mathrm{cm}$ high. If the thickness of the wood is $0.75 \mathrm{cm}$. Find the weight of the wood supposing that $1 {\mathrm{cm}}^3$ of wood weights $0.9 \mathrm{g}$.

When a bus started from the $1\mathrm{st}$ stop, the number of male passengers to number of female passengers was $3 : 1$. At the $1\mathrm{st}$ stop $16$ passengers got down and $6$ more female passengers got in. The ratio of male and female now became $2 : 1$. What was the total number of passengers in the bus when it started from the first stop?

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.

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?

What should come in the place of ($?$) for the expression given below?

$\sqrt{8}+2\sqrt{32}-3\sqrt{128}+4\sqrt{50}=?$

Take $\sqrt{2} =1.414$

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?

$A$ started a business investing $₹250000$ in year $2008$. In year $2009$ he invested an additional amount of $₹100000$ and $B$ joined him with an amount of $₹350000$. In year $2010$, $A$ invested another additional amount of $₹100000$ and $C$ joined them with an amount of $₹350000$. What will be $B\text{'}s$ share in the profit of $₹1500000$ earned at the end of three years from the start of the business in $2008$?

A and B run a kilometre and A wins by $25$seconds. A and C run a kilometre and A wins by $275 m$. When B and C run the same distance, B wins by$30$ seconds. The time taken by A to run a kilometre is

If$(x-y)$is $6$ more than$(w+z)$ and $(x+y)$ is $3$ less than$(w-z)$, then $(x-w)$ is _____.

Water comes to Delhi from river Yamuna in a pipe of radius $21 \mathrm{m}$. If water flows at a uniform rate of $5 \mathrm{kpmh}$. How many litres pass through the pipe in a $\min$?

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?

A train can travel $20\%$ faster than a car. Both start from point A at the same time and reach point B, $75 \mathrm{km}$ away from A at the same time. On the way, however, the train lost about $12.5$ minutes while stopping at the stations. The speed of the car is$:$

Three taps, A, B and C, can fill a tank in $20$, $30$ and $40$ minutes, respectively. All the taps are opened simultaneously, and after $5$ minutes, tap A is closed and then after another $6$minutes, tap B is closed. At the moment, a leak developed, which can empty the full tank in $60$ minutes. What is the total time required for the tank to get completely full?

Pipe A takes $2/3$ of the time required by pipe B to fill the tank individually. When an outlet Pipe C is also opened simultaneously with pipe A and pipe B, it takes $75\%$ more time to fill the empty tank than it takes when only pipe A and B are opened together. If it takes $30$ hours to fill when all the three pipes are opened together, then in what time can pipe C empty the full tank operating alone?

Pipe A alone fills the tank in $x$ hours and Pipe B alone fills the tank in $(x – 8)$ hours. If the efficiency of pipe B is double that of pipe A and pipe A fills the tank at $50$ liters per hour, then what is the capacity of the tank?

Two pipes A and B can fill a tank in $20$ and $30$ minutes respectively. Both the pipes are opened together but after $5$ minutes pipe B is closed. What is the total time required to fill the tank

Two pipes P and Q can fill a tank in $36$ and $24$ minutes respectively. If both the pipes are opened simultaneously, after how much time pipe Q should be closed so that tank is full in $30$ minutes.