$A, B$ and $C$ are three pipes connected to a tank. $A$ and $B$ together fill the tank in $6$ $hrs$. $B$ and $C$ together fill the tank in $10$ $hrs$,and $C$ and $A$ together fill the tank in $7 \frac{1}{2}$ $hrs$. In how much time (in $hours$) will $A, B$ and $C$ fill the tank together?

$10$ buckets of water fill a tank when the capacity of each bucket is $12$ litres. How many buckets will be needed to fill the same tank,if the capacity of each bucket is $8$ litres?

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

In what time would a cistern be filled by three pipes whose diameters are $1 \text{ cm}$,$1 \frac{1}{3} \text{ cm}$,and $2 \text{ cm}$,running together,when the largest alone will fill it in $61 \text{ minutes}$,the amount of water flowing in by each pipe being proportional to the square of its diameter? (in $\text{minutes}$)

Two pipes $A$ and $B$ can fill a tank in $30$ $minutes$ and $45$ $minutes$ respectively. Pipe $C$ can empty the tank in $36$ $minutes$. Initially,pipes $A$ and $B$ are opened. After $12$ $minutes$,pipe $C$ is also opened. What is the total time (in $minutes$) required to fill the tank?

Inlet $A$ is four times faster than inlet $B$ to fill a tank. If inlet $A$ alone can fill it in $15$ minutes,how long will it take if both the pipes are opened together? (in minutes)