Questions
2 questions per paper
Difficulty
Medium
Importance
High scoring potential for SSC and Bank PO exams
Overview
Mixtures and Partnerships are fundamental pillars of quantitative aptitude that test your ability to balance ratios and distributed investments. Mastering the Alligation method and proportional profit-sharing models is essential for solving complex arithmetic problems quickly within tight exam timeframes.
Rule of Alligation
Alligation is a shortcut method to find the ratio in which two ingredients of different prices or concentrations are mixed to produce a mixture of a given mean price. This technique is faster than algebraic linear equations and is the primary tool for mixture problems.
- Mean Value = (Cheaper price * Quantity of cheaper) + (Dearer price * Quantity of dearer) / (Total quantity)
- Ratio = (Dearer Price - Mean Price) : (Mean Price - Cheaper Price)
- The mean value must always lie between the cheaper and dearer values
- Applicable to mixtures of liquids, alloys, and weighted averages
Successive Replacement
This subtopic deals with problems where a part of a liquid is removed and replaced by another, repeated over several cycles. Instead of calculating step-by-step, use the standard formula for concentration decay.
- Final concentration of original liquid = Initial * (1 - (Quantity removed / Total volume))^n
- n represents the number of replacement operations performed
- The ratio of final concentration of liquid to original liquid is independent of the absolute volume if proportions are maintained
Partnership Profit Sharing
Profit in a partnership is distributed based on the product of the investment amount and the time duration for which the capital was utilized. If time is constant, profit is shared directly in the ratio of investments.
- Profit Ratio = (Investment A * Time A) : (Investment B * Time B) : (Investment C * Time C)
- If time is equal, Profit A : Profit B = Investment A : Investment B
- Active partners may receive a fixed salary/bonus before distributing the remaining profit
- Ensure all time units (months vs years) are converted to the same unit before calculating
Formula Sheet
Profit = Investment * Time
Amount of ingredient A = (Quantity of Mixture * % of A) / 100
Final quantity = Initial * (1 - x/V)^n
Exam Tip
Always visualize the Alligation cross-method to verify the ratio order; remember that the difference between the mean and the individual values is always positive.
Common Mistakes
- Failing to convert all time periods into the same unit (months/years) in partnership problems.
- Applying the Alligation rule to percentages or ratios without ensuring they represent the same base unit.
- Forgetting to subtract the 'removed amount' from the total volume in successive replacement questions.
More Revision Notes
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