Alligation - IBPS PO and clerks prep series free

 This article is a part of Free IBPS PO and clerks prep series.

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. 

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.

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.
Let's assume water is available for free,
Cost price of mixture sold is 50 *80/100= 40, as 1/4 profit on sales price = 1/5 profit on cost price.
As you can see, by just deducting weighted average cost from cost of component and vice verse, we arrive at ratio of components used.

Application of Alligation in Time and distance

Problem 3
A man travels part of his journey by bicycle at 20 Km/h and remaining distance by car at speed of 70 Km/h covering the entire journey at an average speed of 50 Km/h. What is the ratio of distance covered by bicycle and car?


Solving this problem by alligation is a matter of just a few seconds, here’s how.

As you can see in the picture, weighted average speed is 50 km/h so we keep it in the middle. Average speed of bicycle and car is taken as in visual components. We take average speed of bicycle on the left side and average speed of car on the right side (rule of thumb). By solving this simple alligation we find that ratio of time the man takes to complete the journey by bicycle and car is 2:3. But here we need to find the ratio of distance covered, so 2*20= 40 and for car 3*70=210

Ratio comes out to be 4:21.

Update - 10-October-2013 (Question requested by Chitra Salin)
Problem 4 - This is from the practice section from PERCENTAGE notes given in website..pls help to solve either in alligation method or any

A water tank contains 5% salt by weight. x litres of fresh water is added to 40 litres of tank water, so that the solution contains 2% salt. The value of x is

a) 40 b) 50 c) 55 d) 60

Solution -
Percentage of water in current mixture = (100 - 5) = 95%
Percentage of water in output mixture = (100 - 2 ) = 98%

Ratio of mixture and fresh water is 2:3. If there was 40 litres of mixture already available in the tank, we need add 40 ×  3/2 = 60 litres
So the answer is D 

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