Alligation is one of the most universal shortcuts in quantitative aptitude. It connects mixtures, averages, profit/loss and even simple interest through a single visual "X" cross. This guide explains the best alligation method shortcut tricks with examples you can use in Bank PO, SSC CGL and Railway exams.
Table of Contents
The Visual "X" Cross Method
When two groups with values A and B are mixed to give a mean value M, the ratio of quantities is:
(cheaper)
(dearer)
Ratio = (B − M) : (M − A)
Example 1: Mixtures
Question: Rice at ₹40/kg is mixed with rice at ₹60/kg to sell the mixture at ₹50/kg. Find the mixing ratio.
| Cheaper (A) | Dearer (B) | Mean (M) | Ratio |
|---|---|---|---|
| ₹40 | ₹60 | ₹50 | (60−50) : (50−40) = 10:10 = 1:1 |
Example 2: Averages
Question: The average age of 20 boys is 14 years and of 30 girls is 16 years. Find the combined average.
Using weighted average: (20×14 + 30×16) ÷ 50 = (280 + 480) ÷ 50 = 760 ÷ 50 = 15.2 years.
Using alligation ratio 20:30 = 2:3 and values 14, 16, we get mean = 14 + (3/5)×2 = 15.2 years.
Example 3: Profit & Loss
Question: Two articles are sold at the same price. One gives 20% profit, the other 10% loss. What is the overall profit/loss percentage?
Assume selling price = ₹100 each.
CP of first = 100/1.20 = ₹83.33
CP of second = 100/0.90 = ₹111.11
Total CP = ₹194.44, Total SP = ₹200
Profit % = (5.56/194.44)×100 ≈ 2.86% profit.
Alligation shortcut (SP same): overall ratio 1:1, profit/loss values +20 and −10. Mean = (20 − 10)/2 = +5% on SP basis, but converting to CP basis gives ≈ 2.86% profit.
Example 4: Simple Interest
Question: Two equal sums are lent at 8% and 12% simple interest. The average rate of interest is 10%. Find the ratio of sums.
| Rate 1 | Rate 2 | Average | Ratio of Sums |
|---|---|---|---|
| 8% | 12% | 10% | (12−10) : (10−8) = 1:1 |
Learn Alligation + 50 More Shortcuts
Shortcut Maths Arithmetic batch covers percentages, profit-loss, SI/CI, time-work and mixtures using visual methods.
Join Batch Call 9804490328FAQs
Q1. Can alligation be used when more than two groups are mixed?
Direct alligation works for two groups. For three or more, use weighted average or apply alligation step-by-step.
Q2. What does the ratio represent in mixture problems?
It represents the ratio of quantities (by weight, volume or amount) of the cheaper and dearer components.
Q3. Is alligation asked in Bank PO Prelims?
Yes, usually as 1-2 questions under arithmetic or DI sections. In Mains it appears in data interpretation sets.
Last updated: June 27, 2026. For coaching in Kolkata, call +91-9804490328.