Eduqo
Quantitative Aptitude›Ch 1: Arithmetic Foundations›Partnership and Mixture-Alligation
Master profit sharing, alligation rule, and mixture replacement for competitive exams.
Profit is always shared in the ratio of capital multiplied by time. Alligation balances two concentrations to find a mean value. Mixture replacement calculates pure quantity left after successive removals.
Quick Memory Hooks
| Topic | Basic Formula | Key Application |
|---|---|---|
| Partnership | P1:P2 = C1T1 : C2T2 | Annual profit division |
| Alligation | (R2 - M) : (M - R1) | Mixing two prices |
| Replacement | V(1 - x/V)^n | Milk and water dilution |
Capital × Time
(Investment weightage)
Investment weightage
Double time gives double share for same capital.
Cross Method
(Alligation cross rule)
Alligation cross rule
Subtract diagonally to get quantity ratio.
Successive
(Repeated removal)
Repeated removal
Apply the fraction multiplier multiple times.
Mean Price
(Intermediate value)
Intermediate value
Mean price must lie between cheaper and dearer.
Adding absolute profits directlyUsing capital-time product ratio
Partnership share depends on duration of investment, not just money put in.
Subtracting mean from cheaper directlyAlways take absolute difference (Greater - Smaller)
Alligation differences are always positive quantities.
Applying replacement formula for water addedFormula gives pure milk left, not water added
Be careful whether the question asks for remaining pure liquid or added liquid.
Q1.A invests Rs. 5000 for 8 months and B invests Rs. 6000 for 6 months. Find their profit sharing ratio.
Q2.In what ratio must tea at Rs. 60/kg be mixed with tea at Rs. 100/kg to get a mixture worth Rs. 75/kg?