# Mixture Problems — Free Timed Practice | Quant Daily > Practise mixture problems free and timed: hold the unchanged part fixed, rebuild the ratio, and read a worked solution every time. No sign-up, no calculator. Source: https://quantdaily.app/drill-types/mixture-problems --- Mixtures ## Mixture problems — track the quantity that does not change Mixture problems give a ratio of two components and then change one of them. Convert the ratio to actual amounts using the stated total, add or remove only what the question changes, and rebuild the ratio from the new amounts. The component that was not touched is your anchor, because its quantity is identical before and after. Almost every mixture question is a ratio question wearing a story. The story tempts you to re-solve the whole thing after the change, when in fact one of the two components never moved. Candidates who spot the fixed component finish in fifteen seconds; candidates who do not end up solving two ratio problems instead of one. **Try it against the clock.** Mixtures runs at 90s easy, 105s medium and 120s hard. The clock is stamped and judged on our server, so the limit you see is the deadline that is actually enforced — and it starts when you tap Start, not while the question is loading. [Start a timed Mixtures drill →](https://quantdaily.app/?drill=mixtures&src=seo-mixture-problems) ### How to solve mixture problems by anchoring on the fixed component - Turn the ratio into real amounts first A 5:1 milk-to-water mixture of 18 litres is 15 litres of milk and 3 of water. Ratios cannot be added to; amounts can. Skipping this step is why the arithmetic goes wrong later. - Change only what the question changes Adding 3 litres of water takes the water from 3 to 6 and leaves the milk at 15. The milk is the anchor — it is untouched, so you never need to recompute it. - Rebuild and reduce the new ratio 15:6 reduces to 5:2. Reducing matters because the unreduced form is almost always printed as a distractor next to the reduced one, and both look correct at a glance. - For price mixing, use alligation instead When two priced goods are blended to a target price, the ratio is the cross-difference: first:second equals |second − mean| : |first − mean|. Note the inversion — the cheaper good takes the larger share. ### Which quantity stays fixed when a mixture changes | The question does this | The anchor is | | --- | --- | | Water is added | The milk amount is unchanged | | Milk is added | The water amount is unchanged | | Pure solvent is added | The solute amount is unchanged | | Some mixture is removed | Nothing is fixed — both fall in ratio | | Two priced goods are blended | The total value is conserved | ### 3 sample mixture problems, with worked solutions Generated by the same engine that mints the Quant Daily daily. Each answer is computed from the numbers printed in the question, and the walkthrough below each one is the engine's own working — not a solution written afterwards. Reload this page's live drill and you get different numbers. #### Question 1 A 25% solution is mixed with a 50% solution to produce a 45% solution. In what ratio must they be mixed? - 4:1 - 5:21 - 1:3 - 1:4 - 1:5 - Alligation: first:second = |second − mean| : |first − mean| = 5 : 20. - Reduce: 1:4. - Answer: 1:4. #### Question 2 A 10% solution is mixed with a 60% solution to produce a 25% solution. In what ratio must they be mixed? - 35:16 - 7:2 - 3:7 - 7:4 - 7:3 - Alligation: first:second = |second − mean| : |first − mean| = 35 : 15. - Reduce: 7:3. - Answer: 7:3. #### Question 3 A solution has concentrate and water in the ratio 4:2. 3 liters of water are added. The original mixture is 18 liters. What is the new concentrate-to-water ratio? - 4:5 - 2:1 - 5:3 - 4:3 - 4:7 - Original: 12 concentrate/milk and 6 water. - Add 3 water → 12 : 9. - Reduce: 4:3. - Answer: 4:3. ### Common mistakes this drill is built from The wrong options are not random numbers. Each one is the result of a specific careless error for this topic, so picking one tells you which habit is costing you marks. #### Adding litres directly to a ratio Treating 5:1 as though adding 3 gives 5:4 skips the conversion to real amounts entirely. The ratio parts are not litres until you scale them by the total. #### Leaving the answer unreduced 15:6 and 5:2 are the same ratio, but only one is printed as the key. The unreduced form is a deliberate distractor in nearly every set. #### Getting the alligation ratio backwards In price mixing the share of the first good is driven by the second good's distance from the mean. The inverted answer is always an available option. ### Why your answer came out wrong The specific wrong numbers this topic produces, and what each one tells you about the step you took. If you have just got a question wrong and want to know which habit did it, start here. #### A 5:1 mixture of 18 litres gets 3 litres of water. Is the new ratio 5:4? No — it is 5:2. The 18 litres split as 15 milk and 3 water, so adding 3 water gives 15:6, which reduces to 5:2. Adding the 3 to the ratio part instead of the litres is the single most common error here, and 5:4 is printed as an option. #### I got 15:6 and it was not in the options. Did I make a mistake? Your arithmetic was right; you just stopped one step early. 15:6 reduces to 5:2, and the key is always the reduced form. Make reducing the last reflex before you read the options rather than the first thing you skip under time pressure. #### For blending goods at 25 and 80 to reach a mean of 45, is the ratio 20:35? The distances are |80 − 45| = 35 and |45 − 25| = 20, and the ratio of the first to the second is 35:20, which reduces to 7:4. Writing 20:35 inverts it. The cheaper good takes the larger share because the mean sits nearer to it. ### FAQ #### What is the fastest way to handle adding water to a mixture? Convert the ratio into actual quantities using the total, then change only the water. The milk is untouched, so it carries straight through and the new ratio is the new water amount against the original milk amount. Reduce before you look at the options. #### Why does the cheaper item get the larger share in alligation? Because the ratio is built from distances to the mean, and it is inverted. If the mean sits closer to the dearer price, the mixture must contain more of the cheaper good to pull the average down. The cross-difference rule encodes that inversion for you. #### Do I need the actual total to solve these? For a ratio-to-ratio question you often do, because you cannot add a real quantity to an abstract ratio part. When a total is given, use it. When it is not, the question is usually pure alligation and the ratio alone is enough. ### Practise the next topic - [All 51 drill types](https://quantdaily.app/drill-types) — the shared daily cycles 36 of 51, with every published time limit. - [Ratio word problems — chain two ratios through the shared term](https://quantdaily.app/drill-types/ratio-word-problems) — ratio word problems, timed. - [Percentage questions](https://quantdaily.app/drill-types/percentages) — percentage questions, timed. - [Speed tricks](https://quantdaily.app/drill-types) — the seven mental-math shortcuts that make a 15-second answer possible. - [How to improve calculation speed](https://quantdaily.app/calculation-speed) — the six-week arc these drills fit into. Quant Daily is free, needs no account, and is not affiliated with ETS or GMAC. GRE/GMAT-style practice only.