Mixture & Alligation
Mixture & Alligation
Mixture problems combine ingredients at different prices or concentrations; alligation finds the mixing ratio without equations. SSC CGL Tier 1, Tier 2, and banking exams each carry 1\u20132 mixture questions. Repeated dilution and profit-based alligation are the hardest and most frequently tested variants. Draw the alligation cross every time \u2014 it eliminates algebra entirely.
Key Idea
Draw the alligation cross: put C1 top-left, C2 top-right, mean price Cm in centre. The diagonal differences give the mixing ratio: (C2 − Cm) : (Cm − C1).
Core Formulas
Alligation Rule (Mixing Ratio)
Ratio = (C2 − Cm) : (Cm − C1) where Cm is the mean/target value
Find the mixing ratio of two ingredients at different prices or concentrations \u2014 place the target value in the centre of the alligation cross and read off the ratio from the diagonal differences.
Repeated Dilution
Pure liquid remaining = V × ((V − x) / V)ⁿ
Apply when x litres are removed and replaced with water n times from a V-litre container \u2014 plug values directly into the formula instead of tracking each round separately.
Weighted Average (Mixed Mixture)
Resultant Avg = (n₁×p₁ + n₂×p₂) / (n₁ + n₂)
When combining two mixtures of different sizes and concentrations.
Milk-Water Problem
Milk% in final mix = Total milk / Total volume × 100
After repeated replacement or combination — track milk and water separately.
Mean Price Constraint
C1 < Cm < C2 (mean price must lie between the two ingredient prices)
To verify the problem setup — if Cm is outside this range, something is wrong.
Relevant Exams
Mixture & Alligation is a consistent topic in SSC CGL Tier 1 and Tier 2, and banking exams. Repeated dilution and profit-based alligation are the hardest and most frequently asked variants.