2.10 How to Approach an Unseen Mixtures Question — A Decision Checklist

When you meet a mixtures-and-alligation question you haven’t seen before, run through these questions in order — they will point you to the correct row of the formula table within a few seconds:

1. Are exactly two prices/concentrations and a mean given, and is a ratio asked for? → Use the two-ingredient criss-cross diagram (Section 2.1).
2. Are three or more prices given along with their quantities (or a fixed ratio), and is a single mean price/value asked for? → Use the direct weighted-average formula (Section 2.2, Type A).
3. Does the question mention something being “withdrawn and replaced with water” (or another liquid) and repeated a number of times? → This is the replacement formula (Section 2.3). Identify P (constant total), x (amount removed each time) and n (number of repetitions) before writing anything else.
4. Are two or more already-mixed containers being poured into one another? → Convert every container’s contents into actual quantities of each component and add them (Sections 2.2/2.7) — never average the ratios directly unless you have explicitly verified the volumes are equal.
5. Does the question mention a selling price and a profit or loss percentage on a mixture? → First convert SP and profit/loss% into a mean cost price using the box formula in Section 2.5, and only then apply alligation.
6. Does the question involve adding or removing a pure ingredient (not a mixture) to change a ratio? → A direct ratio equation (Section 2.6) is usually faster than alligation here, since one component’s quantity stays fixed throughout.
7. Does the question talk about “average speed,” “average marks,” or another averaging context outside of prices? → Check first whether the averaging is by time/count (use alligation, Section 3 Trick 7/8) or by equal distance (use the harmonic mean instead, Section 4’s common mistake) — this single check prevents the most costly error in the whole chapter.

Working through this checklist for the first 8–10 unfamiliar questions you attempt will make pattern recognition automatic well before exam day.