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Quadratic Equations — Maths STD 10 — Question

Gujarat BoardEnglish MediumSTD 10MathsQuadratic Equations4 Marks
Question
If two pipes function simultaneously, a reservoir will be filled in $12$ hours. One pipe fills the reservoir $10$ hours faster than the other. How many hours will the second pipe take to fill the reservoir?
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Answer

Two pipes can fill the, reservoir in $= 12$ hours
Let first pipe can fill the reservoir in$ = x$ hrs
Then second pipe will fill it in $= (x - 10)$ hours
Now according to the condition,
$\frac{1}{\text{x}}+\frac{1}{\text{x}-10}=\frac{1}{12}$
$\Rightarrow\frac{\text{x}-10+\text{x}}{\text{x}(\text{x}-10)}=\frac{1}{12}$
$\Rightarrow\frac{2\text{x}-10}{\text{x}^2-10\text{x}}=\frac{1}{12}$
$ \Rightarrow x^2-10 x=24 x-120 $
$ \Rightarrow x^2-10 x-24 x+120=0 $
$ \Rightarrow x^2-34 x+120=0 $
$ \Rightarrow x^2-30 x-4 x+120=0 $
$ \Rightarrow x(x-30)-4(x-30)=0 $
$ \Rightarrow(x-30)(x-4)=0$
Either $x - 30 = 0$, then $x = 30$
Or $x - 4 = 0$ but it is not possible as it is $< 10$
The second pipe will fill the reservoir in $= x - 10 = 30 - 10 = 20$ hours.

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