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.

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?

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

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

Take $\sqrt{2} =1.414$

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?

$A$ 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 boat has to travel upstream $20 \mathrm{km}$ distance from point X of a river to point Y. The total time taken by the boat in travelling from point X to Y and Y to X is $4$ minutes and $40$ seconds. What is the speed of the boat?

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 _____.

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$:$

If $\frac{3}{16}$ of a tank is filled in $15$ minutes, the rest of the tank will be filled in

Taps A and C can fill a tank in $5$ and $20$ hrs respectively. Taps B and D can drain a full tank in $10$and $40$hrs. respectively. If A, B, C and D are opened in a gap of $2$ hrs. in that order the tank gets full in______.

Two pipes A and B can fill an empty tank in $10 \mathrm{hours}$ and $16 \mathrm{hours}$, respectively. They are opened alternately for $1 \mathrm{hour}$ each, opening pipe B first. In how many hours, will the empty tank be filled?