Question

How many grams of a 5% sulfur ointment must be mixed with 180 grams of 20% sulfur ointment to prepare an 8% sulfur ointment?

Answer: [a] g of 5% sulfur ointment (#g)  Do not round

Answer 1

Allegation is an arithmetical method of solving problems that involve the mixing of ingredients possessing different percentage strengths. In this method for calculating the quantity of a component of given strength that should be mixed with a specified quantity of another component of given strength to make a preparation of desired strength involves the following steps are required:

· First step is to find relative amount of individual components needed.

The difference between strength of stronger component (20 %) and desired strength (8%) indicates parts of weaker strength to be used.

So 20 - 8 = 12 parts parts of weaker strength

AND

The difference between the desired strength (8%) and the strength of the weaker component (5%) indicates the number of parts of the stronger strength to be used.

So 8 – 5 = 3 parts of stronger strength

Hence the relative amounts of both the strengths of sulphar ointment to be used are

= 3 parts stronger strength : 12 parts weaker strength

=1 : 4

· Second step is calculating required quantity using dilution formula

Dilution formula is

Quantity 1 X Concentration 1 = Quantity 2 X Concentration 2

That is Q1 * C1 = Q2 * C2

=            Q1 / Q2 = C1 / C2

On putting values:

4 Parts/ 1 Part = X grams / 180

On cross multiplication

X = 4* 180 grams

= 720 grams

Hence 720 grams of 5 % sulphur ointment should be added to 180 grams of 20 % sulphur ointment to get ointment of final strength of 8%.