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PTCB Math Practice
PTCB Test Prep

**Alligation is a method used to calculate the proportion of two solutions needed to produce a final solution of required concentration.** **Here, we review PTCB alligation practice problems to help you get to grips with this essential mathematical mechanism.**

If you have two solutions of different concentrations – you can use alligation as a means to establish how much of ** each solution** should be mixed to give you a different or desired concentration.

For example – imagine we have two solutions:

- One solution has a concentration of
**20% w/v** - A second solution has a concentration of
**4% w/v**

Let’s say that we want to mix these two solutions to produce a solution with a concentration of **10% w/v**.

**How much of both solutions should be mixed to produce this third concentration?**

That’s the essence of alligation – *it let’s you work out this kind of problem*.

Pharmacy calculations are an important part of the PTCB test.

Even though there are 90 questions on the exam, only 6-10 of these questions are likely to be pharmacy calculations.

An alligation-style question is likely to appear. Given how much calculation theory and practice need to be prepared for the exam, it’s imperative that students take the time to learn the alligation method and know when the conditions apply to use it in practice.

Of course, this takes time.

If you have not yet worked out **PTCB practice test questions** on alligations, the topic may at first seem complicated. What matters is that you understand the method. If you have the method committed to memory and have practiced many different types of alligation question, things become far, far easier.

Let’s briefly review a sample question that uses the alligation method:

*Q. How many parts of an 20% w/v solution and 8% w/v solution are needed to produce an 10% w/v solution?*

First, you must be able to identify that *alligation can be used*.

In this test question, it asks us to produce a solution of a desired concentration (10% w/v) from mixing two other solutions with different concentrations (20% w/v and 8% w/v).

Yes – the conditions are ripe for alligation.

Once you have identified that this is an alligation question, next you should present the data as you see it.

At PTCB Test Prep, we recommend the following format:

**Solution of Highest Concentration**: 20% w/v**Solution of Lowest Concentration**: 8% w/v**Solution of Desired Concentration**: 10% w/v

Very clearly and easily presented.

Once done, you must follow the alligation method. This involves:

- Subtracting the lower concentration (8 w/v) from the desired concentration (10% w/v) =
**2**(*higher concentration ratio value*) - Subtract the desired concentration (10 w/v) from the higher concentration (20% w/v) =
**10**(*lower concentration ratio valu*e)

This gives us a ratio of **2:10** (higher concentration : lower concentration)

Let’s suppose that the question asked us to **produce 500mL** of 10% w/v solution.

In this case, we know the ratio – **2:10**

In other words, **2 parts higher concentration** to **10 parts lower concentration**.

In other words, there are 12 parts (*2 parts + 10 parts*):

- 2/12 x 500mL =
**83.33mL** - 10/12 x 500mL =
**416.66mL**

In conclusion – to make **500mL of a 10% w/v solution**, we require 83.33mL of the 20% w/v solution and 416.66mL of the 8% w/v solution.

It takes some time to commit the alligation method to memory but, once you have taken enough PTCB alligation practice problems, the method becomes second nature.

To summarize:

**First identify that the problem involves alligation**– typically, this means producing a solution of the desired concentration from two other solutions.**Set out the data**– as per our recommendation, this involves setting out:*Solution of Highest Concentration**Solution of Lowest Concentration**Solution of Desired Concentration*

Of course, all this information is presented in the question.

**Implement the alligation method to find a ratio**:

*Subtract the lower concentration from the desired concentration (H).*

*Subtract the desired concentration from the higher concentration (L).*

The ratio is **H:L**.

**The ratio lets you know how much of each solution is needed**.

For example: a ratio of 2:3 means there are 5 (2+3) parts to the solution. If the solution is 100mL, then 2 out of 5 parts is the higher concentration and 3 out of 5 parts is the lower concentration.

In this case,**40mL and 60mL**respectively.

This is the fundamental mechanism of alligation.

It makes concentration questions much simpler. **It’s all in the method**.

Of course, this is not the only kind of alligation question, but the method can be modified to handle these other kinds of PTCB practice test questions.

As easy as it may be, try not to avoid learning the alligation method.

Yes, it is more difficult and time-consuming than many other pharmacy calculations. For sure. But once you can take a step back and really learn the method, all you need to do during the exam is plug in the values and work out the answer. If anything, it becomes simple.

But like everything, it takes practice.

If you are already a registered member of PTCB Test Prep, you have complete **access to our alligation tutorials** and practice exams as part of our broader *Calculations for Technicians Module*. If you are not yet a member and would like access to this Module, take a few moments to register to one of our three online, self-paced courses.

**In the meantime, check back to PTCB Test Prep soon for more content to help you master the exam and become a licensed, professional pharmacy technician in the United States.**