Question

Two pipes P&Q can fill a cistern in 12 min and 15 min respectable. if both pipe are opened together and at the 3 min. the first is closed. then how much longer will the cistern take to fill? ​

Answer 1

Given :

• Two pipes P & Q can fill a cistern in 12 min and 15 min respectively.
• Both pipes can fill the cistern in 3 mins
• Tap P is closed.

To Find :

• how longer will the cistern take to fill with just one pipe open.

Solution :

Let the time taken to fill the cistern be x min.

The part of the cistern filled in first minute by pipe P → $\mathtt{\dfrac{1}{12}}$

The part of the cistern filled in first minute by pipe Q → $\mathtt{\dfrac{1}{15}}$

Pipe P & Q together :

➣ $\mathtt{\dfrac{1}{12}\:+\:{\dfrac{1}{15}}}$

➣ $\mathtt{\dfrac{15\:+\:12}{12\:\times\:15}}$

➣ $\mathtt{\dfrac{27}{180}}$

➣ $\mathtt{\dfrac{9}{60}}$

➣ $\mathtt{\dfrac{3}{20}}$

$\large{\boxed{\mathtt{\red{Pipe\:P\:and\:Q\:will\:fill\:{\dfrac{3}{20}\:part\:of\:cistern\:in\:1\:min}}}}}$

Part filled by Pipe P in 3 mins :

➣ $\mathtt{3\:\times\:{\dfrac{3}{20}}}$

➣ $\mathtt{\dfrac{9}{20}}$

$\large{\boxed{\mathtt{\pink{Pipe\:P\:will\:fill\:{\dfrac{9}{20}\:part\:of\:cistern\:in\:3\:min}}}}}$

Remaining Part filled in 3 mins :

➣ $\mathtt{1\:-\:{\dfrac{9}{20}}}$

➣ $\mathtt{\dfrac{20-9}{20}}$

➣ $\mathtt{\dfrac{11}{20}}$

Part filled by Pipe Q :

➣ $\mathtt{x\:\times\:{\dfrac{1}{15}={\dfrac{11}{20}}}}$

➣ $\mathtt{\dfrac{x}{15}\:=\:{\dfrac{11}{20}}}$

➣ $\mathtt{20x\:=\:15\:\times\:11}$

➣ $\mathtt{x\:=\:{\dfrac{15\:\times\:11}{20}}}$

➣ $\mathtt{x\:=\:\dfrac{165}{20}}$

➣ $\mathtt{x\:=\:{\dfrac{33}{20}}}$

$\large{\boxed{\mathtt{\blue{The\:cistern\:will\:take\:8.25\:mins\:to\:fill}}}}$