Question

You have a sugar solution (solution A) with concentration x. You pour one-third of this solution into a beaker and add an equivalent volume of water (solution B).
a. What is the ratio of sugar in solutions A and B?
b. Compare the volumes of solutions A and B.
c. What is the ratio of the concentrations of sugar in solutions A and B?

Short answer

• The ratio of sugar in solutions A and B is$4:1$
• The volume of solution B is half that of solution A
• The ratio of the concentrations of sugar in solutions A and B is$2:1$

Step-by-step solution

Definition

The amount of dissolved materialpresent per unit of volume is described as concentration.

Determination of ratio of sugar in solution A and B

a)

x is the amount of sugar in solution A.

The volume of the solutiondrops when one-fourth of it is transferred. As a result, the amount of sugar in solution Bis reduced by four times.

Sugar concentration in the solution$B=\frac{x}{4}$

Calculate the sugar content of solutions A and B.

$\begin{array}{c}\frac{Sugar\text{inA}}{Sugar\text{inB}}=\frac{x}{\frac{x}{4}}\\ =\frac{4}{1}\end{array}$

As a result, the sugar ratio in solutions A and B is $4:1$.

Comparing the volumes of solution A and B

b)

Let’s take volume of solution $A=x$

Here the volume of solution $B=\frac{x}{2}$

Thusthe volume in solution B is half than that of volume in solution A.

Determining of ratio of the concentrations of sugar in solution A and B

c)

Sugar solution A has a concentration of x.

The volume of the solution drops when one-fourth of it is transferred. As a result, the amount of sugar in solution B is reduced by four times.

Sugar content in a solution $B=\frac{x}{4}$

The concentration of sugar in solution B was determined by dilutingit with thesame amount of water.

As a result, after solution, the concentration of solution $B=\frac{x}{2}$

Let’s compute the sugar content of solutions A and B.

$\begin{array}{c}\frac{Sugar\text{inA}}{Sugar\text{inB}}=\frac{x}{\frac{x}{2}}\\ =\frac{2}{1}\end{array}$

As a result,the sugar concentration ratio in solutions A and B is $2:1$.[pk1]