Question

9. Three taps M, N and C are opened together. If M fills the tank in 2 hours, N fills it in 3 hour
and third tap C empty it in 6 hours. Then in how much time will they take to fill it up
the tank?​

Answer 1

$\underline{\underline{\huge{\gray{\tt{\textbf Answer :-}}}}}$

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$\sf\large\bold{\orange{\underline{\blue{ Given :-}}}}$

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• Tap M can fill the tank in 2 hours

• Tap N can fill the tank in 3 hours

• Tap C can empty the tank in 6 hours

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$\sf\large\bold{\orange{\underline{\blue{ To \: Find :-}}}}$

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• Time taken to fill the tank when all the taps are opened together

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$\sf\large\bold{\orange{\underline{\blue{ Solution :-}}}}$

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Let the time taken to fill the tank when all the taps are opened together be "a"

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$\underline{\bold{\texttt{1 hour work of tap M :}}}$

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Given that , Tap M can fill the tank in 2 hours

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➠ $\sf \dfrac { 1 } { 2 }$

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$\underline{\bold{\texttt{1 hour work of tap N :}}}$

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Given that , Tap N can fill the tank in 3 hours

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➠ $\sf \dfrac { 1 } {3 }$

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$\underline{\bold{\texttt{1 hour work of tap C :}}}$

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Given that , Tap C can empty the tank in 6 hours

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➠ $\sf \dfrac { 1 } { 6 }$

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$\underline{\bold{\texttt{1 hour work when all taps were opened :}}}$

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➜ $\sf \dfrac { 1 } { 2 } + \dfrac { 1 } { 3 } - \dfrac { 1 } { 6 }$

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➜ $\sf \dfrac { 3 + 2 - 1 } { 6 }$

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➜ $\sf \dfrac { 4 } { 6 }$

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➜ $\sf \dfrac { 2 } { 3 }$

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$\underline{\bold{\texttt{"a" hour work when all taps are opened :}}}$

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As we assumed that the tank is filled in "a" hours when all the taps were opened

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So,

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➜ $\sf \dfrac { 2 } { 3 } \times a = 1$

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➜ $\sf 2a = 3$

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➜ $\sf a = \dfrac { 3 } { 2 }$

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➨ a = 1.5

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• Hence time taken to fill the tank when all the taps are opened together is 1.5 hours

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