Questions
1 question per paper
Difficulty
Medium
Importance
Low weightage but a high-speed solving tool
Overview
Mixtures and Alligation is a time-saving technique used to determine the ratio in which two ingredients of different prices or concentrations are mixed to produce a resultant mixture of a known mean price. Mastering this concept is crucial for SSC and Banking exams because it significantly reduces the time required to solve problems related to percentages, profit and loss, and simple interest. The core idea relies on the inverse ratio of the deviations of individual concentrations from the mean concentration.
The Alligation Rule
Alligation is an application of the weighted average formula to find the ratio of quantities. It is applicable when two items are mixed to form a third, intermediate value.
- Formula: (Quantity of Cheaper / Quantity of Dearer) = (Mean Price - Cheaper Price) / (Dearer Price - Mean Price)
- The mean value must always lie between the values of the two ingredients.
- The difference should always be taken as (Greater Value - Smaller Value).
- The result gives the ratio of the quantities, not the absolute amounts.
Mixing Two Mixtures
When dealing with two mixtures containing the same components in different proportions, we convert everything to a single component basis to apply alligation.
- Focus on only one component (e.g., milk only or water only) to setup the equation.
- Convert ratios to fractions: (Component A / Total Mixture).
- The denominator must be the same for all three values before subtracting.
- Use fractional values to avoid errors with complex percentages.
Mean Price and Replacement Problems
These are common in SSC exams where a part of the mixture is replaced by pure liquid multiple times. This requires a specific iterative formula.
- Formula for 'n' replacements: Final Amount = Initial Amount * (1 - (Quantity Replaced / Total Quantity))^n
- Replacement only works if the amount withdrawn equals the amount added.
- Keep the ratio of the final concentration constant if multiple replacements occur.
- Identify the 'n' number of repetitions clearly before applying the power rule.
Formula Sheet
Q1/Q2 = (d - m) / (m - c)
Final Quantity = Initial * (1 - x/V)^n
Exam Tip
Always verify that the Mean Value lies strictly between the two component values; if it doesn't, your setup is inverted.
Common Mistakes
- Subtracting in the wrong direction and resulting in negative ratios.
- Forgetting to convert ratios into fractions when mixing two mixtures, leading to calculation errors.
- Misinterpreting 'n' as the total quantity instead of the number of replacement cycles in successive dilution problems.
More Revision Notes
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