2-12. ALLIGATION PROBLEMS
a. Example 1: A pharmacist has a 70% alcoholic elixir and a 20% alcoholic
elixir. He needs a 30% alcoholic elixir to use as a vehicle for medications. In what
proportion must the 70% elixir and the 20% elixir be combined to make a 30% elixir?
10 parts of 70%
1 part of 70 %
40 parts of 20%
4 parts of 20 %
50 parts of 30%
5 parts of 30 %
NOTE: *This means that if one part of 70% elixir is mixed with four parts of 20% elixir, it
will yield five parts of 30% elixir. The dotted arrows in the matrix above have been
placed as a reminder that the total number of parts always represents the desired
b. Example 2: In what proportion must plain coal tar be combined with a 2%
coal tar ointment to make a 4% coal tar ointment?
NOTE: Coal tar, because it is pure coal tar and not diluted, will be the higher (100
If one part of coal tar is combined with 48 parts of 2% coal tar ointment,
it will yield 49 parts of 4% coal tar ointment.