Questions
~2 questions per paper
Difficulty
Medium
Importance
High yield for HPCL/NTPC/GAIL
Overview
Mixtures and Alligation is a high-yield arithmetic topic that provides a streamlined shortcut for solving complex weighted average problems. Mastering this technique allows candidates to bypass lengthy algebraic equations, significantly saving time in fast-paced PSU exams like HPCL and NTPC.
The Alligation Rule
Alligation is an application of the weighted average formula, used to find the ratio in which two ingredients are mixed to produce a mixture of a given mean price. It acts as a visual balancing act between the cheaper and dearer prices.
- (Dearer - Mean) : (Mean - Cheaper) = Quantity of Cheaper / Quantity of Dearer
- The mean value must always lie between the individual values of the two ingredients.
- Ensure all units are consistent (e.g., all in price per kg or all in percentage concentration).
Mixing Two Mixtures
This subtopic involves calculating the new composition when two mixtures of the same components with different ratios are blended. The standard approach involves normalizing the total quantity of one component to find the resulting ratio.
- Express each component as a fraction of the total volume.
- Add the respective fractions of the same component from both mixtures.
- Use the ratio of final fractions to determine the new mixture composition.
Successive Dilution and Replacement
A common exam favorite, this involves repeatedly removing a portion of a liquid and replacing it with an equal amount of another. The concentration decreases exponentially over multiple operations.
- Final concentration = Initial amount * (1 - replacement amount / total quantity)^n
- n represents the number of times the replacement process is repeated.
- This formula applies only when the replaced volume is uniform throughout the operations.
Mean Price Problems
These problems focus on finding the price of a mixture given the ratio of ingredients or vice-versa. It is the most frequent application of the Alligation rule in PSU quantitative aptitude sections.
- Mean price = (Total value of all ingredients) / (Total quantity of all ingredients)
- Use Alligation to determine the ratio of weights required to achieve a target profit margin.
- Always calculate the Cost Price (CP) for the mixture, not the Selling Price (SP).
Formula Sheet
Quantity of Cheaper / Quantity of Dearer = (d - m) / (m - c)
Final Amount = Initial Amount * (1 - x/y)^n
Exam Tip
Always verify that your Mean Price is between the Cheap and Dear prices; if it is not, you have swapped your variables or miscalculated.
Common Mistakes
- Using Selling Price instead of Cost Price in the Alligation rule formula, leading to incorrect ratios.
- Forgetting that the replacement formula only accounts for the concentration of the original liquid, not the added liquid.
- Inverting the ratio of the quantities in the Alligation grid, leading to a reversed final result.
More Revision Notes
Ready to test yourself?
Play topic-wise Mixtures & Alligation questions in Aspirant Arcade — gamified MCQ practice.
Download Free