Symbiosis National Aptitude Test SNAP 2013 Paper

Capacity of tank = 2400 ${\mathit{m}}^3$.
Let the emptying capacity of pump = $\mathit{x}{\mathit{m}}^3$/min
then filling capacity of pump = (x – 10) ${\mathit{m}}^3$/min.
then according to problem.
$\frac{2400}{\mathit{x}-10}-\frac{2400}{\mathit{x}}$ = 8
2400 x – 2400 (x – 10) = 8 (x) (x – 10)
⇒ 2400x – 2400x + 24000 = $8{\mathit{x}}^2$ – 80x
⇒ $8{\mathit{x}}^2$ – 80x – 24000 = 0
⇒ ${\mathit{x}}^2$ – 10x – 3000 = 0
⇒ (x – 60) (x + 50) = 0
x = 60
x ≠ 50
Filling capacity of pump = 60 – 10 = 50 ${\mathit{m}}^3$/min.