NTSE Stage 2 MAT 2015 Question Paper

Let first, second and third pipe be A, B & C.
According to question,
$\mathrm{B}=\mathrm{A}-5$ ...(i)
$\mathrm{B}=\mathrm{c}+4$ ...(ii)
Let the time required by the first pipe to fill the tank be x hr
From equation (i)
$\mathrm{B}=\mathrm{x}-5$
From equation (ii)
$\mathrm{c}=\mathrm{x}-9$
Again According to question
$\frac{1}{\mathrm{A}}+\frac{1}{\mathrm{B}}=\frac{1}{\mathrm{C}}$
$\frac{1}{\mathrm{x}}+\frac{1}{\mathrm{x}-5}=\frac{1}{\mathit{x}}-9$
$\left(2\mathrm{x}-5\right)\left(\mathrm{x}-9\right)=\mathrm{x}\left(\mathrm{x}-5\right)$
${\mathrm{x}}^2-18\mathrm{x}+45=0$
${\mathrm{x}}^2-15\mathrm{x}-3\mathrm{x}+45=0$
$\mathrm{x}\left(\mathrm{x}-15\right)-3\left(\mathrm{x}-15\right)=0$
$\mathrm{x}=3=0$
∴ $\mathrm{x}=3$ is not possible
∴ $\mathrm{x}-15=0$ ∴ $\mathit{x}=15$
So, the time required by the first pipe to fill the tank is 15 hours.