Question

A bottle contains 10 mL of a 40 mg/2.5 mL medicine solution. How many mL of thesolution should be poured out and replaced with pure water to have 10 mL of 30mg/2.5 mL solution?

Answer 1

Suppose the bottle contains x units of medicine and y units is taken out and replaced with water. The expression to find the the amount of pure medicine solution after replacement by n times is given by

$\begin{gathered} \text{The amount of pure medicine remaining, v=} \\ x(1-\frac{y}{x})^n \\ \end{gathered}$

In the given question, v =30mg, x=40 mg.

n=1, since replacement is done only one time. We have to find y.

Substitute values in equation.

$\begin{gathered} 30=40(1-\frac{y}{40})^1 \\ \frac{30}{40}=\frac{40-y}{40} \\ 30=40-y \\ y=40-30 \\ =10mg \\ \end{gathered}$

So, 10 mg/2.5 ml solution is poured out and replaced with water