Quantitative Aptitude Notes : Averages, Mixtures & Alligation

Averages, Mixtures & Alligations is one of the most important topics in quantitative aptitude section in various SSC and Banking exams. In this blog post, we will cover all the important aspects of this topic.

1. Simple Average

Average = Sum of Observations / Number of Observations

Another effective way to calculate the average ( avoids large calculations ) is given by the following formula :-

Average = Assumed Average + [ ( Sum of deviations ) / Number of Observations ]

Here, you can assume any number to be the average and the deviations are calculated from that number. It is advisable to assume a number that lies some where in the middle of the data set to be the average so as to reduce calculations.

2. Weighted Average

For the given formula, ‘p’ denotes the property and ‘q’ denotes the quantity. Weighted average can be thought of as the final property of the desired mixture.

Weighted Average =  ( p1.q1 + p2.q2 ) / ( q1 + q2 )

• Here, instead of taking the exact quantities, one can also use their ratio to simplify calculations.
• The deviation method to calculate average ( as discussed above ) can also be used here.

Consider the following formula:-

Weighted Average = Assumed Average + ( Deviations x Ratio of Quantities ) / ( Ratio of Quantities )

Use the formula for weighted averages when the focus of the question is on the property of the resultant mix.

3. Alligation

The formula for alligation must be use when the focus of the given question is to find the quantities in the resultant mix. Here,

X : Y = Quantity of Dearer : Quantity of Cheaper

Alligation rule helps us to find, in what ratio two mixtures with different concentrations are to be mixed to get a target concentration. 

4. Formula For Solution Replacement

$FC=IC{(1-\frac{\mathrm{x/}}{v})\; ^}^n$

Consider the following question,

A flask contains alcohol solution with concentration 18%.  If 6 Liters of this mixture is taken out and replaced with water, then concentration drops to 15%.  Suppose this process is repeated 3 times. What is the original volume in the flask?

As per the given question, we have to find the intial concentration of the flask.

Thus,

FC = Final Concentration ( In this case 18 % )

IC = Initial Concentration ( In this case, to be found )

x  =  Quantity Replaced ( In this case, 6L )

v  =  Total Volume

n  =  Number of time the replacement is performed

Take a quick test on averages, mixtures & alligation here.

Hope this helps.

All the best!