A jug has 1 litre of 10% strength cordial. How much pure cordial needs to be added to make the strength 20%?

The volume or amount of pure cordial to be added to the solution to make the strength 20% is 125 ml

Step-by-step explanation:

The given parameters, are;

The volume of cordial in the jug = 1 litre

The percentage strength of the cordial = 10%

The proportion of the cordial that contains pure cordial = 0.1

Therefore, the volume of pure cordial in the jug = 0.1 × 1 = 0.1 × 1000 ml = 100 ml

The volume of the solvent = The volume of the solution -  The initial volume of pure cordial

∴ The volume of the solvent = 1000 ml - 100 ml = 900 ml

To increase the concentration of the cordial to 20% is given by the relation;

x/(x+900) = 0.2

Where;

x = The total volume of the pure cordial to be added to the pure solvent

Solving, gives;

x = 0.2×(x+900) = 0.2·x + 180

x -0.2·x = 180

0.8·x = 180

x = 180/0.8 = 225 ml

The total volume of the pure cordial to be added to the pure solvent = x = 225 ml

Therefore, the volume of pure cordial to be added to the initial volume of pure cordial in the solution, which is 100 ml, is therefore given as follows;

The volume or amount of pure cordial to be added = 225 ml - 100 ml = 125 ml.

The volume or amount of pure cordial to be added = 125 ml