If two pipes function simultaneously,the reservoir will be filled in $12$ $hours$. One pipe fills the reservoir $10$ $hours$ faster than the other. How many $hours$ does the faster pipe take to fill the reservoir?

Two pipes $A$ and $B$ can fill a tank in $20$ $minutes$ and $30$ $minutes$ respectively. If both the pipes are used together,then how long will it take to fill the tank? (in $minutes$)

Two pipes $A$ and $B$ can fill a cistern in $18$ $minutes$ and $9$ $minutes$ respectively,while a third pipe $C$ can empty the full tank in $5$ $minutes$. $A$ and $B$ are kept open for $4$ $minutes$ in the beginning and then $C$ is also opened. In what time (in $minutes$) is the cistern emptied?

$A$ big tanker can be filled by two pipes $A$ and $B$ in $60$ and $40$ $min$ respectively. What time will it take to fill an empty tanker if tap $B$ is used for half of the total time and both taps $A$ and $B$ together are used for the remaining half of the time?

Two pipes $A$ and $B$ can fill a tank in $30$ $minutes$ and $45$ $minutes$ respectively. Pipe $C$ can empty the full 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?

Three pipes $A$,$B$,and $C$ can fill a cistern in $10$,$12$,and $15$ $hours$,respectively,while working alone. If all the three pipes are opened together,the time taken to fill the cistern will be: