Question

8. Pipe A can fill a tank in 5 hours but another pipe B can empty it in 8 hours. If both pipes opened
together, then how much time take to fill 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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• Pipe A can fill a tank in 5 hours

• Pipe B can empty it in 8 hours

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

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• Time required to fill the tank when both the pipe are opened together

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

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Let time required to fill the tank when both the pipe are opened together be "x"

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$\underline{\bold{\texttt{One hour work of Pipe A :}}}$

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Given that , Pipe A can fill a tank in 5 hours

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➠ $\sf \dfrac { 1 } { 5 }$

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$\underline{\bold{\texttt{One hour work of Pipe B :}}}$

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Given that , Pipe B can empty it in 8 hours

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➠ $\sf \dfrac { 1 } { 8}$

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$\underline{\bold{\texttt{One hour work when both pipe are opened :}}}$

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➜ $\sf \dfrac { 1 } { 5 } - \dfrac { 1 } { 8 }$

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➜ $\sf \dfrac { 8 - 5 } { 40 }$

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➜ $\sf \dfrac { 3} { 40 }$

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$\underline{\bold{\texttt{"x" hour work when both pipe are opened :}}}$

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➜ $\sf \dfrac { 3} { 40 } \times x = 1$

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➜ $\sf x = \dfrac { 40 } { 3 }$

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➨ x ≈ 13.3 hours

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• Hence when both pipes are opened they can fill the tank in approx 13.3 hours

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