Question

Three pipes A, B and C can fill a tank in 12 hours, 15 hours and 20 hours respectively. How long wou
three pipes take to fill the empty tank, if all of them are opened together?
​

Answer 1

$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

$\:\:$

$\large{\green{\underline \bold{\tt{Given :-}}}}$

$\:\:$

• Pipe A can fill the tank in 12 hours

$\:\:$

• Pipe B can fill the tank in 15 hours

$\:\:$

• Pipe C can fill the tank in 20 hours

$\:\:$

$\large{\red{\underline \bold{\tt{To \: Find :-}}}}$

$\:\:$

• Time taken by three pipes to fill the empty tank, if all of them are opened together

$\:\:$

$\large{\orange{\underline{\tt{Solution :-}}}}$

$\:\:$

• Let the time taken by three pipes to fill the empty tank be "x"

$\:\:$

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

$\:\:$

➠ $\sf \dfrac { 1 } { 12 }$

$\:\:$

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

$\:\:$

➠ $\sf \dfrac { 1 } { 15 }$

$\:\:$

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

$\:\:$

➠ $\sf \dfrac { 1 } { 20 }$

$\:\:$

$\underline{\bold{\texttt{One hour work of all three pipes opened together :}}}$

$\:\:$

➜ $\sf \dfrac { 1 } { 12 } + \dfrac { 1 } { 15 } + \dfrac { 1 } { 20 }$

$\:\:$

➜ $\sf \dfrac { 5 + 4 + 3 } { 60 }$

$\:\:$

➜ $\sf \dfrac { \cancel {12} } { \cancel {60} }$

$\:\:$

➜ $\sf \dfrac { 1 } { 5 }$

$\:\:$

$\underline{\bold{\texttt{x hour work of all three pipes opened together :}}}$

$\:\:$

➜ $\sf \dfrac { 1 } { 5 } \times x$

$\:\:$

〚 As we assumed that if all three pipes are opened for "x" hours they will fill the empty tank 〛

$\:\:$

So,

$\:\:$

➜ $\sf \dfrac { 1 } { 5 } \times x = 1$

$\:\:$

➨ x = 5 hours

$\:\:$

• Hence if all three pipes are opened together they will fill the empty tank in 5 hours

Answer 2

$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

$\:\:$

$\large{\green{\underline \bold{\tt{Given :-}}}}$

$\:\:$

• Pipe A can fill the tank in 12 hours

$\:\:$

• Pipe B can fill the tank in 15 hours

$\:\:$

• Pipe C can fill the tank in 20 hours

$\:\:$

$\large{\red{\underline \bold{\tt{To \: Find :-}}}}$

$\:\:$

• Time taken by three pipes to fill the empty tank, if all of them are opened together

$\:\:$

$\large{\orange{\underline{\tt{Solution :-}}}}$

$\:\:$

Let the time taken by three pipes to fill the empty tank be "x"

$\:\:$

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

$\:\:$

➠ $\sf \dfrac { 1 } { 12 }$

$\:\:$

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

$\:\:$

➠ $\sf \dfrac { 1 } { 15 }$

$\:\:$

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

$\:\:$

➠ $\sf \dfrac { 1 } { 20 }$

$\:\:$

$\underline{\bold{\texttt{One hour work of all three pipes opened together :}}}$

$\:\:$

➜ $\sf \dfrac { 1 } { 12 } + \dfrac { 1 } { 15 } + \dfrac { 1 } { 20 }$

$\:\:$

➜ $\sf \dfrac { 5 + 4 + 3 } { 60 }$

$\:\:$

➜ $\sf \dfrac { \cancel {12} } { \cancel {60} }$

$\:\:$

➜ $\sf \dfrac { 1 } { 5 }$

$\:\:$

$\underline{\bold{\texttt{x hour work of all three pipes opened together :}}}$

$\:\:$

➜ $\sf \dfrac { 1 } { 5 } \times x$

$\:\:$

〚 As we assumed that if all three pipes are opened for "x" hours they will fill the empty tank 〛

$\:\:$

So,

$\:\:$

➜ $\sf \dfrac { 1 } { 5 } \times x = 1$

$\:\:$

➨ x = 5 hours

$\:\:$

• Hence if all three pipes are opened together they will fill the empty tank in 5 hours