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Alligation alternate questions are a common type of problem in quantitative aptitude, especially in competitive exams. Mastering these questions requires understanding key formulas and concepts that simplify the solving process. This article provides essential formulas to help students crack alligation alternate questions effectively.
Understanding Alligation Alternate Method
The alligation alternate method involves combining two or more quantities with different concentrations or values to achieve a desired average or concentration. The core idea is to use the difference between the quantities and the target value to find the proportions.
Key Formulas for Alligation Alternate Questions
1. Difference Method Formula
For two quantities, the ratio of their parts is given by:
Parts of Quantity 1 = Difference between the other quantity’s value and the target value
Parts of Quantity 2 = Difference between the first quantity’s value and the target value
Mathematically:
Ratio of quantities = (Difference from Quantity 2 to Target) : (Difference from Quantity 1 to Target)
2. General Alligation Formula
For multiple sources, the average or concentration is calculated using:
Average or Target Value = (Sum of all quantities’ values weighted by their parts) / (Total parts)
Practical Application of Formulas
Use these formulas to quickly determine the ratio of different sources or quantities involved in the problem. Remember, the differences are always taken with respect to the target value or average you need to achieve.
Example Problem and Solution
Suppose a mixture of two types of solutions, one containing 40% alcohol and the other 80%, is prepared to get a mixture of 60% alcohol. Find the ratio of the two solutions used.
Solution:
- Difference between 80% and 60% = 20%
- Difference between 40% and 60% = 20%
Ratio of solutions = 20 : 20 = 1 : 1
Therefore, equal parts of both solutions are mixed to get the desired concentration.
Conclusion
Mastering these essential formulas simplifies alligation alternate questions, enabling quick and accurate solutions. Practice regularly to familiarize yourself with different scenarios and improve problem-solving speed.