Question

Tap $A$ can fill a water tank in 12 min, tap $B$ will fill the same tank in 10 min and tap $C$ can empty the tank in 6 min. If all the three taps are opened together, in how many minutes will the tank be completely filled up or emptied?

• A. $15$min
• B. $30$ min
• C. $45$ min
• D. $60$ min

Answer 1

The correct option is D $60$ min

Part of the tank filled by A in 1 min $=\frac { 1 }{ 12 }$

Part of the tank filled by B in 1 min $=\frac { 1 }{ 10 }$.

Part of the tank filled when the three taps are opened together $=\left(\frac{1}{12}+\frac{1}{10}-\frac{1}{6}\right)=\frac{5+6-10}{60}=\frac{11-10}{60}=\frac{1}{60}$

$\therefore$ If all the three taps are opened together, then the tank will be filled in $60$ minutes.