Management Aptitude Test Sep 2013 Paper

(b) 85% of 73 L of wine = $\frac{85\times 73}{100}$
Now, let the process is repeated n times
Then,
$\frac{85\times 73}{100}$ > $\left[73\times {\left(1-\frac{3.65}{73}\right)}^{\mathit{n}}\right]$
∵ Quantity of liquid left = $\left[\mathit{a}{\left(1-\frac{\mathit{b}}{\mathit{a}}\right)}^{\mathit{n}}\right]$
Where a is initial content of liquid and b is amount of liquid replaced
= $\frac{85\times 73}{100}$ > $\left[73\times {\left(1-\frac{3.65}{73}\right)}^{\mathit{n}}\right]$
⇒ $\frac{85}{100}>{\left(\frac{73-3.65}{73}\right)}^{\mathit{n}}$
⇒ $\frac{17}{20}>{\left(\frac{69.35}{73}\right)}^{\mathit{n}}$
⇒ $\frac{17}{20}>{\left(\frac{19}{20}\right)}^{\mathit{n}}$
⇒ 0.85 > ${\left(0.95\right)}^{\mathit{n}}$
On solving n > 3
∴ Minimum 4 operations are required.