Alligation Shortcuts Tricks

Alligation method is a simplified method to solve complex average problems. Alligation also helps simplify Ratio and Proportion, Simple and compound interest, Profit and loss, Time & Distance, Time Work problems among others. For better understanding, a few illustrations are given below. We take weighted average in the middle and average of components on the upper left and upper right hand side resulting in ratio.

Problem

A class of consists of 60 boys and 50 girls. Average weight of boys is 60 kgs and of girls is 40 kgs. Calculate average weight of the class.

Solution

You can solve this question either by traditional weighted average method or you can simplify the calculations by using alligation.
60-x/x-50 = 2/3
X = 56

By solving this question by alligation by taking individual averages above, as in this case 60 kg and 40 kg is individual averages(don’t know what you meant by this, correct it yourself). Take smaller average on the left hand side and bigger average on the right hand side. This is just a rule of thumb to avoid mistakes and make things easier. We always take weighted average in the middle. Then by deducting individual average from weighted average and vice versa we arrive at ratios at which these components were used.

Problem 2

There’s almost always a question on mixtures in a number of competitive exams. Here’s an example.

In what ratio should water be mixed with wine worth Rs. 60 per litre so that the seller earns a profit of 25% after selling the mixture for Rs. 50 per litre.