Three taps $A, B$ and $C$ can fill a tank in $12, 15$ and $20$ hours respectively. If $A$ is open all the time and $B$ and $C$ are open for one hour each alternately,the tank will be full in? (in hours)

$A$ pipe fills a water tank three times faster than another pipe. If the two pipes together can fill the empty tank in $36$ $minutes$,then how much time will the slower pipe alone take to fill the tank?

Two pipes $A$ and $B$ can fill a tank in $24$ $minutes$ and $32$ $minutes$ respectively. If both the pipes are opened simultaneously,after how much time (in $minutes$) should $B$ be closed so that the tank is full in $18$ $minutes$?

$A$ water tank has three taps $A, B, C$. Tap $A$,when opened,can fill the water tank alone in $4$ hours. Tap $B$,when opened,can fill the water tank alone in $6$ hours,and tap $C$,when opened,can empty the water tank alone in $3$ hours. If taps $A, B,$ and $C$ are opened simultaneously,how long (in hours) will it take to fill the tank completely?

Two pipes $A$ and $B$ together can fill a cistern in $4$ $hours$. Had they been opened separately,then $B$ would have taken $6$ $hours$ more than $A$ to fill the cistern. How much time (in $hours$) will be taken by $A$ to fill the cistern separately?

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 $\text{minutes}$)