Exam path · Mixture & Alligation
Mixture and alligation questions give two quantities of different strength — percentages, prices or a concentrate-to-water ratio — and ask for the ratio to mix them in, or the result of adding more of one. The cross-gap rule settles the mixing ratio in one line: first-to-second is the gap from the second value to the mean, to the gap from the first value to the mean, in that order.
Mixture and alligation is a short, formulaic corner of banking and SSC quant, typically one or two marks, and it rewards a single rule learned properly more than any other topic in the section. The two question shapes — mix two strengths to hit a target, or add water to change a ratio — cover nearly everything the paper asks, and the cross-gap rule below is the same trick behind both.
Try it against the clock. Mixtures runs at 40s easy, 50s medium and 65s 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.
The question names a first value and a second value, in that order, then the mean the mixture ends up at. Keep that order — the ratio you compute has to answer 'first to second', not 'cheap to dear'.
Ratio first:second = |second − mean| : |first − mean|. Each value's gap decides how much of the other value is used — that crossing is the whole rule.
A ratio of 20:40 and one of 1:2 are the same mixing instruction, so cancel common factors before matching your answer to the options.
When water is added to a mixture, the concentrate amount never changes. Work out how much concentrate and water are present in litres first, add the new water to the water side only, then re-express as a ratio.
| What the paper says | What it means |
|---|---|
| Two solutions of x% and y% mixed to z% | Ratio x:y = |y − z| : |x − z| |
| Two goods at ₹x/kg and ₹y/kg mixed to ₹z/kg | Same cross-gap rule, with price standing in for percentage |
| Milk and water in ratio m:w, water added | Milk stays fixed; only the water figure grows |
| Only the water figure is asked for after dilution | Convert to litres, add the new water to that side only, then re-ratio |
Generated by the same engine that mints the ComputePrep 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.
A mixture contains milk and water in the ratio 4:2.
2 litres of water is added.
The original mixture is 12 litres.
What is the new milk-to-water ratio?
A mixture contains milk and water in the ratio 3:1.
3 litres of water is added.
The original mixture is 12 litres.
What is the new milk-to-water ratio?
A mixture contains milk and water in the ratio 3:2.
4 litres of water is added.
The original mixture is 10 litres.
What is the new milk-to-water ratio?
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.
The stem's order is first-then-second, not cheap-then-dear. If the dearer item happens to be named first, swapping the parts by habit gives the ratio inverted — a clean, wrong answer that is always among the options.
If milk and water start at 3:1 and 4 litres of water are added, the new ratio is not 3:5. Convert to actual litres first — say 12 and 4 — then add the 4 litres of water to get 12:8, which reduces to 3:2.
The gap from the second value to the mean gives the share of the first, and vice versa. Matching each gap to its own value instead of the other one is the single most common slip in this topic.
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.
Because the stem names 20% first and 80% second, and the rule answers first:second in that order. The gaps to the mean are |80−40|=40 and |20−40|=20, giving 40:20, which reduces to 2:1 — not 1:2, which is what crossing them the wrong way produces.
Cross the gaps in the order the stem names the prices: ₹80 first, ₹20 second. The gap from the second price to the mean is |20−40|=20, and from the first price to the mean is |80−40|=40, so first:second = 20:40 = 1:2. Assuming the pricier item automatically takes the larger share gives 2:1, which is wrong.
The ratio numbers are not litres. With the original mixture at 16 litres, 3:1 means 12 litres of concentrate and 4 of water. Adding 4 litres of water makes it 12:8, which reduces to 3:2 — not 3:5, which comes from adding 4 straight onto the ratio's water term instead of the actual litres.
Ratio first:second = |second − mean| : |first − mean|. Take the gap from each named value to the mean and cross them: the gap on one side gives the share of the other. It works identically whether the values are percentages, prices or concentrations.
Yes. They are a standard arithmetic topic in IBPS, SBI and SSC quantitative aptitude, usually one or two marks, split between mixing-ratio questions and replacement questions where part of a mixture is drawn off and replaced with water.
About 40 to 65 seconds in prelims, which is what this drill enforces on the server: 40 seconds on easy, 50 on medium and 65 on hard.
One rule covers it: cross the gaps to the mean. There is no separate formula for prices versus percentages versus concentrations — the same cross-gap ratio applies to all three.
Yes, free with no account needed. Every question is generated fresh from the engine, so the numbers are never the same twice.
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