Question

Pipes $A$ and $B$ can fill a tank in $5$ hours and $6$ hours respectively. Another pipe $C$ can empty the tank in $12$ hours. If all the three pipes are opened together, how much time will it take to fill the tank?

Answer 1

LCM$(5,6,12)=60$

Suppose capacity of the tank is $60$l. Then, quantity filled by pipe A in $1$hr $=\frac{60}{5}=20$l

Quantity filled by pipe B in $1$hr $=\frac{60}{6}=10$l

Quantity filled by pipe C in $1$hr $=\frac{60}{12}=5$l

Quantity filled in $1$hr if all the three pipes are opened together$=12+10-5=17$l

Required time$=\frac{60}{17}=3\frac{9}{17}$hrs.