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Home » Two pipes running together can fill a tank in minutes. If on pipe takes 5 minutes more than the other to fill the tank separately, find the time in which each pipe would fill the tank separately.
Two pipes running together can fill a tank in 11 \frac{1}{9} minutes. If on pipe takes 5 minutes more than the other to fill the tank separately, find the time in which each pipe would fill the tank separately.
CBSE | Class 10 | Exercise 10e | Maths | Quadratic Equations | RS Aggarwal
Two pipes running together can fill a tank in 11 \frac{1}{9} minutes. If on pipe takes 5 minutes more than the other to fill the tank separately, find the time in which each pipe would fill the tank separately.

Let the time taken by one pipe to fill the tank be x minutes.

\therefore Time taken by the other pipe to fill the tank =(x+5) \min

Suppose the volume of the tank be V.

Volume of the tank filled by one pipe in x minutes =V

\therefore Volume of the tank filled by one pipe in 1 minute=\frac{V}{x}

\Rightarrow Volume of the tank filled by one pipe in 11 \frac{1}{9} minutes =\frac{V}{x} \times 11 \frac{1}{9}=\frac{V}{x} \times \frac{100}{9}

Similarly,

Volume of the tank filled by the other pipe in 11 \frac{1}{9} minutes =\frac{V}{(x+5)} \times 11 \frac{1}{9}=\frac{V}{(x+5)} \times \frac{100}{9}

Now,

Volume of the tank filled by one pipe in 11 \frac{1}{9} minutes +
Volume of the tank filled by the other pipe in 11 \frac{1}{9} minutes =V

\begin{array}{l} \therefore V\left(\frac{1}{x}+\frac{1}{x+5}\right) \times 100=V \\ \Rightarrow \frac{1}{x}+\frac{1}{x+5}=\frac{9}{100} \\ \Rightarrow \frac{x+5+x}{x(x+5)}=\frac{9}{100} \\ \Rightarrow \frac{2 x+5}{x^{2}+5 x}=\frac{9}{100} \\ \Rightarrow 200 x+500=9 x^{2}+45 x \\ \Rightarrow 9 x^{2}-155 x-500=0 \\ \Rightarrow 9 x^{2}-180 x+25 x-500=0 \\ \Rightarrow 9 x(x-20)+25(x-20)=0 \\ \Rightarrow(x-20)(9 x+25)=0 \\ \Rightarrow x-20=0 \text { or } 9 x+25=0 \\ \Rightarrow x=20 \text { or } x=-\frac{25}{9} \end{array}

\therefore x=20

(Time cannot be negative)

Time taken by one pipe to fill the tank =20 \mathrm{~min}.

Time taken by other pipe to fill the tank =(20+5) 25 \mathrm{~min}

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