Standard Bank Ltd. || TAO (20-07-2018) || 2018

প্রশ্নে বলা হচ্ছে যে, 60 লিটারের একটি মিশ্রণে দুধ ও পানি 2 : 1 অনুপাতে আছে। কতটুকু পানি মেশালে দুধ ও পানির অনুপাত 1 : 2 হবে?

Sum of the given ratio = 2 + 1 = 3

∴ Quantity of milk $= \left(60 of \frac{2}{3}\right) = 40 liters$

Hence, quantity of water will be = 60-40 = 20 liters

Assume, x liters water needs to be added.

∴ According to question, $\frac{40}{x+20} = \frac{1}{2}$

$$\begin{gathered} \Rightarrow x+20 = 80 \\ \Rightarrow x = 80 - 20 = 60 \\ \therefore x = 60 \\ So, 60 liters water needs to be added. \end{gathered}$$

Given x = 3 +22

$$\begin{gathered} \Rightarrow x = 25 \\ \Rightarrow 5^2 = x \\ \Rightarrow 5 = \sqrt{x} \\ \therefore \sqrt{x} = 5 \\ Now, \sqrt{x} - \frac{1}{\sqrt{x}} \\ = 5 - \frac{1}{5} \left[Putting the value of \sqrt{x}\right] \\ = \frac{25-1}{5} \\ = \frac{24}{5} \\ \therefore \sqrt{x} - \frac{1}{\sqrt{x}} = \frac{24}{5} \end{gathered}$$