1. Introduction

Mixtures and Alligation is one of the most reliable scoring topics in the SSC and Railway quantitative aptitude sections. On average, SSC CGL, CHSL, and MTS papers carry 1–2 direct questions from this chapter, while RRB NTPC and Group D papers carry 1–3, and the topic also sneaks into disguised forms inside Profit-Loss, Time-Speed-Distance, and Data Interpretation questions. The reason examiners love it is simple: alligation is a single, elegant rule that replaces three or four lines of simultaneous equations with one criss-cross diagram, so it rewards students who have memorised the method and punishes those who try to solve it from scratch with algebra under time pressure.

Difficulty-wise, this chapter sits in the “easy-to-moderate” band for basic two-ingredient alligation, but climbs to “moderate-to-hard” once questions combine alligation with repeated replacement (the classic “milk withdrawn and replaced with water n times” problem), with three or more ingredients, or with profit-loss and average concepts layered on top. The good news is that almost every question in this chapter, however dressed up, reduces to one of a small number of standard templates — once you recognise the template, the arithmetic is usually just clean fractions and ratios.

This chapter builds directly on two topics you have already studied: Ratio (because the output of every alligation calculation is a ratio) and Average (because the “mean price” in alligation is nothing but a weighted average, and several of the shortcut tricks in this chapter are just alligation applied to averages instead of prices). If your Ratio and Average fundamentals are solid, Mixtures and Alligation should feel like a natural, fast extension rather than new territory. Keep your ratio-simplification skills (HCF, cross-multiplication) sharp — they are used in almost every single problem below.

From an exam-strategy standpoint, this chapter deserves a specific kind of practice: not just solving problems, but drilling the criss-cross diagram until you can write down a ratio in one line without thinking about the underlying derivation each time. In a 60-minute SSC CGL Tier-1 quant section with 25 questions, a mixtures question should typically cost you 30–45 seconds if it is a straightforward two-ingredient alligation, and at most 90 seconds even for a repeated-replacement or three-ingredient problem. If you find yourself writing out simultaneous equations from scratch during the exam, that is a signal to go back and re-drill the standard templates in this chapter until they become automatic. Pay special attention to the repeated-replacement formula (Section 2.3) and the “reverse alligation on mixtures” pattern (Section 2.2, 2.7) — these two account for the majority of the higher-difficulty questions RRB NTPC and SSC CGL Tier-2 papers ask from this topic.