Today, I want to share some basics of Alligations with you.
It forms one of the topics of study in almost every Quantitative Aptitude Textbook.
Lets begin with a brief know-how : -
Alligation is an old and practical method of solving arithmetic problems related to mixtures of ingredients. There are two types of alligation: alligation medial, used to find the quantity of a mixture given the quantities of its ingredients, and alligation alternate, used to find the amount of each ingredient needed to make a mixture of a given quantity. Alligation medial is merely a matter of finding a weighted mean. Alligation alternate is more complicated and involves organizing the ingredients into high and low pairs which are then traded off.
So, if we have n1 items of average weight w1 and n2 items of average weight w2.
Then, if we mix the items then the combined average weight is given by the formula:-
Aw = (n1 * w1 + n2 * w2)
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(n1 + n2)
Just twisting the formula a bit, we can also arrive at a very helpful corrolary,
n1/n2 = (Aw - w2) / (w1 - Aw)
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Quantitative Aptitude books are filled with relevant questions based on the above theory and the reader can refer the same.
What I am interested at this point is to share some seemingly difficult questions, which become very easy, when we view them from the point of view of Alligations:-
1) Pradeep mixes two mixtures of milk and water. He mixes 40 litres of the first containing 20% water and 60 litres of second containing 30% water. Find the percentage of water in the final mixture.
2) A trader earns a profit of 20% on 40% of his goods sold, while he earns a profit of 30% on 60% of his goods sold. Find his percentage profit on the whole.
3) 40% of the revenues of a school comes from the junior classes while 60% of the revenues of the school came from senior classes.
If the school raises its fees by 20% for the junior classes and 30% for the senior classes, find the percentage increase in the revenues of the school.
Making oneself comfortable with applications of alligations, we can save hell lot of time and energy while we tackle questions in the time-intensive aptitude tests.
Hope the post helps,
Till next time,
Good Bye and Take Care,
Ashish
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