Question

You have a 70% solution and a 15% solution, and you are asked to make 480ml of a 30% solution. What parts of each strength will be used, and give the final volume of each needed for the prescription.

Answer 1

As in the question two initial concentrations of solutions are provided, we need to solve it via alligation calculations which is also known as TicTac Toe calculations.

Given:
70% : higher strength
15% : lower strength
30 % : desired/final strength
480 ml : desired/final volume

First we need to draw the alligation grid i.e. similar to a 3x3 tic-tac-toe board and we need to fill it by following convention:

→ The higher strength goes in the top left box.
→ The lower strength goes in the bottom left box.
→ The desired strength goes in the center box.

70
	30
15

Now the numbers that goes into the top right and bottom right boxes is calculated by working diagonally and taking the difference between the two numbers already in place. One thing that needs to be taken into note is that only positive numbers can go into the grid. So:

70-30=40

and

15-30=-15 (Change it to 15)

Now entering these values

70		40
	30
15		15

Alligation ratio is calculated from 3^rd column numbers i.e.

40:15

or

8:3

Now this ratio gives us the number of parts of each strength that will be used.

So 8 parts of 70% solution and 3 parts of 15% solution will be used to make 30% solution.

Now to answer 2^nd part of the question i.e. to calculate volume of each solution

we can simply determine it by dividing each solutions part needed by total parts and then multiplying it with total volume required i.e. 480 ml:

So for 70% solution:

8/11 X480 = 349.09 ml

and for 15% solution

3/11 X 480 = 130.90 ml