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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
15min
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B
30 min
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C
45 min
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D
60 min
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Solution

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 $$= \left( \displaystyle\frac { 1 }{ 12 } + \displaystyle\frac { 1 }{ 10 } - \displaystyle\frac { 1 }{ 6 }  \right) = \displaystyle\frac { 5+6-10 }{ 60 } = \displaystyle\frac { 11-10 }{ 60 } = \displaystyle\frac { 1 }{ 60 }$$

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

Mathematics

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