The Irony of Our Education System
Consider the troubling paradox at the heart of modern curricula: alligation—the mathematical technique for mixing and adulterating products—is presented as essential knowledge, taught as a noble skill to be mastered and treasured. Yet this very technique, when applied in the real world, enables deception, exploitation, and the systematic corruption of the consumer trust that holds society together.
This is more than a mathematical curiosity. This is a societal evil that deserves careful examination.
What Is Alligation, Really?
On the surface, alligation is simply a faster computational method for solving weighted average problems—scenarios where two groups with different characteristics are combined. It appears harmless enough in textbooks and educational assessments.
But the troubling truth becomes apparent when you examine the practical problems used to teach this concept. Consider the standard textbook question: “A dishonest milkman sells milk at cost price but adulterates it with water, gaining a 25% profit. What percentage of the mixture is water?” This is not a hypothetical academic exercise. This question normalizes deception. It teaches students the precise mathematics of cheating—how to systematically defraud customers while maximizing personal profit.
The Educational System’s Complicity
The inclusion of alligation across virtually all major quantitative examinations is deeply troubling. When educational institutions—which should be moral guardians of society—repeatedly teach students how to calculate the optimal levels of adulteration and deception, they are doing far more than teaching mathematics. They are normalizing fraud as an acceptable practice worthy of mastery.
This isn’t theoretical concern. The pervasiveness of product adulteration in markets across the world—contaminated milk, diluted fuel, adulterated spices—suggests that these mathematical lessons translate directly into real-world harm. We have systematized the teaching of deception, and society has paid the price.
The Mathematics of Alligation
Despite these ethical concerns, understanding the technique is necessary to navigate a world where such practices are common. The alligation method provides an elegant solution to weighted average problems:
Alligation Equation: When two groups with averages a and b are mixed in quantities x and y to produce an average of c:
x/y = (b − c)/(c − a)
Weighted Average Formula: Weighted Average = (Sum of all group values) / (Total number of elements)
Visual Method 1: The Cross Diagram
When all three averages are known and you need to find the ratio of quantities being mixed, the cross diagram provides an intuitive visual approach:
- Place the average of the first group (a) on the left
- Place the average of the second group (b) on the right
- Place the resulting average (c) in the center
- The diagonal differences reveal the proportional quantities
This graphical method is effective for quick calculations, though its very efficiency enables the rapid optimization of adulterant mixtures—exactly the kind of calculation that harms consumers.
Visual Method 2: The Straight-Line Approach
When one of the averages is unknown, the straight-line method proves more practical:
Visualize a number line with positions a, b, and c arranged in order:
- y corresponds to the distance (c − a) — representing the proportion of the first group
- x corresponds to the distance (b − c) — representing the proportion of the second group
- (x + y) corresponds to the total distance (b − a) — representing the combined quantity
This adaptation makes the technique flexible across different problem structures.
A Practical Example: The Problem We Should Question
The standard textbook example asks: “A dishonest milkman professes to sell milk at cost price but mixes it with water, gaining a 25% profit. What percentage of the mixture is water?”
Stop and reflect on what this question teaches. It teaches students:
- How to calculate the exact proportion of adulterant needed
- That deception can be scientifically optimized
- That systematic fraud against consumers is a worthy intellectual exercise
This is not mathematics education. This is training in systematic deception.
The Real-World Consequences
The gap between textbook problems and reality is devastatingly small. Consider:
- How many of us can honestly say we consume pure milk in today’s marketplace?
- How certain can we be that the petrol in our vehicles is genuine, or if it’s been diluted with cheaper kerosene?
- How many spices, oils, and essential products are routinely adulterated with fillers, water, or toxic substitutes?
These are not rhetorical questions. They reflect the daily reality of millions of consumers who cannot trust the basic products they purchase for their families’ health and safety. The mathematical technique that solves these adulteration problems with elegance is the very tool that enables this widespread harm.
The Moral Failure of Educational Systems
This is where the critique becomes fundamental: How can we expect a moral and truthful society if our educational systems systematically teach students the mathematics of deception?
Educational institutions have a responsibility beyond curriculum delivery. They must ask themselves: What values are we reinforcing when we celebrate mastery of adulteration calculations? What message do we send when dishonesty is presented as a mathematical puzzle to be solved?
The irony is profound. We teach these techniques under the guise of “logical thinking” and “problem-solving,” but we’re actually training the next generation of people who will apply these skills to harm others for profit. We’re creating a culture where the most clever person is not the one who builds trust, but the one who optimizes deception most efficiently.
Why We Must Learn This Despite These Concerns
Understanding alligation becomes almost obligatory in modern education, not because it’s valuable knowledge for an honest society, but because:
- It’s embedded in standardized assessments that determine educational and career outcomes
- It appears in professional and business contexts where such optimization might be relevant
- Understanding it helps us recognize and resist such practices when we encounter them in the market
But learning this technique should come with a clear moral framework: this is how deception works mathematically, and understanding it should strengthen our resolve to reject it in practice, not embrace it.
The Path Forward
Alligation is a mathematical tool. Like all tools, it can be used constructively or destructively. The tragedy is that our educational system has chosen to teach it almost exclusively in contexts of deception and fraud.
A genuinely moral education would:
- Teach alligation transparently, acknowledging its historical use in enabling fraud
- Explore how legitimate industries (pharmaceuticals, food science, quality control) use weighted averaging for honest purposes
- Challenge students to consider the ethical implications of optimization problems
- Develop critical thinking that questions why we’re solving a particular problem, not just how
The choice is ours. We can continue normalizing the mathematics of deception, or we can demand that educational systems teach these skills within a framework of moral accountability. Until we do, we will continue to live in a society where adulteration is not a crime of ignorance, but a carefully calculated business practice—one whose mathematics we’ve taught to millions of students.
