Rahul Chaudhary

About Rahul Sir Rahul Sir is a renowned Aptitude and Reasoning trainer with extensive experience preparing students for competitive examinations such as IBPS PO, IBPS Clerk, SBI PO, SBI Clerk, SSC, Railways, and other government exams. Known for his simple teaching style and practical shortcut techniques, he helps students solve complex aptitude problems quickly and accurately. His teaching focuses on building strong fundamentals, improving calculation speed, and mastering exam-oriented tricks that save valuable time during competitive exams. Through structured lessons, real exam questions, and regular practice sessions, Rahul Sir has guided thousands of aspirants toward achieving their career goals. In this article, Rahul Sir breaks down one of the most scoring yet often misunderstood topics in Quantitative Aptitude — Alligation and Mixture — into simple, exam-ready techniques that you can apply within seconds during your IBPS PO and Clerk exams. 1. What is Alligation and Why It Matters in Banking Exams Alligation is a mathematical technique used to solve problems involving the mixing of two or more ingredients, quantities, or values that have different properties — such as price, concentration, or ratio — to find a resultant mixture with a specific average value. In IBPS PO and Clerk exams, Alligation questions typically appear in the Quantitative Aptitude section and can involve mixing liquids of different prices, milk-water solutions, different grades of items, or even average-based problems disguised as mixtures. This topic is important because it usually takes candidates a long time to solve using conventional algebraic methods, but with the Alligation rule, the same question can be solved in under 20 seconds. Banking exams are highly time-sensitive, with candidates having roughly a minute or less per question, so mastering a fast method for mixture problems gives you a real edge over other aspirants. Alligation questions are also popular because examiners can twist them in many ways — replacement of mixtures, mixing more than two components, or combining alligation with ratio-proportion and profit-loss concepts. Understanding the core logic thoroughly, rather than memorizing formulas blindly, ensures you can adapt to any variation the exam throws at you, making this one of the highest-value topics to master for scoring well in the Quant section. 2. The Basic Alligation Rule (Formula and Logic) The foundation of solving any Alligation question lies in one simple rule: the ratio in which two quantities at different values must be mixed to produce a mixture at a given average value is inversely proportional to the difference of the extreme values from the average value. The standard formula is written as: Quantity of Cheaper : Quantity of Dearer = (Dearer Value − Mean Value) : (Mean Value − Cheaper Value) This is best visualized using the well-known Alligation Cross Method, where the cheaper value (C) and dearer value (D) are placed at the top two corners, the mean value (M) is placed in the middle, and the differences (D − M) and (M − C) are cross-multiplied diagonally to get the ratio. For example, if a shopkeeper mixes tea worth ₹60/kg with tea worth ₹80/kg to get a mixture worth ₹68/kg, the ratio of cheaper to dearer tea is (80−68):(68−60) = 12:8 = 3:2. This means for every 3 units of the ₹60 tea, you need 2 units of the ₹80 tea. Rahul Sir emphasizes that students should not just memorize this formula but understand why it works — the mean value always divides the mixture in inverse proportion to how far each component’s value is from the average. Once this logic is internalized, even unfamiliar or twisted questions become manageable within seconds, without needing to write a single equation. 3. Alligation Cross Method — Step-by-Step Visual Trick The Alligation Cross Method is the single most powerful visual shortcut for solving mixture problems quickly, and Rahul Sir recommends practicing it until it becomes second nature. Here’s how to apply it step by step: Step 1: Draw a cross (X) diagram. Write the cheaper quantity’s value at the top-left corner and the dearer quantity’s value at the top-right corner. Step 2: Write the mean (average) value of the final mixture in the center of the cross. Step 3: Subtract diagonally — subtract the mean value from the dearer value, and write this result at the bottom-left corner (this becomes the ratio of the cheaper quantity). Then subtract the cheaper value from the mean value, and write this at the bottom-right corner (this becomes the ratio of the dearer quantity). Step 4: The bottom-left and bottom-right numbers, simplified, give the required ratio of cheaper to dearer quantities. Example: A trader mixes two varieties of rice costing ₹40/kg and ₹60/kg to make a mixture worth ₹52/kg. Using the cross method: (60−52):(52−40) = 8:12 = 2:3. So the cheaper rice and dearer rice must be mixed in a 2:3 ratio. This visual method eliminates the need for algebraic equations entirely. Rahul Sir advises students to practice drawing this cross quickly on rough paper during mock tests until they can compute the ratio mentally within 10-15 seconds, which is essential given the strict time constraints of IBPS PO and Clerk exams. 4. Solving Mixture Problems Involving Milk and Water One of the most frequently tested variations of Alligation in IBPS exams involves milk-and-water mixtures, where a vessel contains milk mixed with water in a certain ratio, and candidates must find the ratio needed to achieve a desired concentration, or determine how much water must be added or removed. For pure milk-water problems, treat pure milk as having a “value” of 100% (or 1) and water as having a “value” of 0%, then apply the same alligation cross rule using percentages instead of prices. Example: In what ratio should a milkman mix pure milk with water to get a mixture that is 80% pure milk? Using alligation: pure milk = 100%, water = 0%, mean = 80%. Ratio = (100−80):(80−0) = 20:80 = 1:4. So milk and water should be mixed in a 1:4 ratio. A trickier variant involves mixing two different milk solutions,