Quantitative Aptitude Mixture and Alligation Practice for All Exams
Mixture and alligation questions test how quickly you can compare quantities, prices, concentrations and ratios. They appear regularly in SSC, banking, insurance, railway, postal and civil service examinations, often alongside averages, percentages and profit-and-loss problems.
The central idea is simple: when two ingredients with different values are combined, the final value lies between their individual values. The alligation rule turns this relationship into a quick ratio, while the mixture method helps calculate the actual quantities, cost or concentration.
Australian examples can make the topic easier to visualise. You may compare coffee beans sold at a Melbourne market, petrol prices in Sydney, milk sold by the litre, or mineral products associated with Western Australia. The units may change, but the mathematics remains the same.
Use exact figures, keep units consistent and identify whether the question asks for a ratio, quantity, price or percentage. Competitive exams reward an organised method more than lengthy calculations.
| Situation | Key comparison | Useful method |
|---|---|---|
| Two prices produce a mean price | Differences from the mean | Alligation |
| Two concentrations produce a final concentration | Differences from the final value | Alligation |
| Several quantities are combined | Total value ÷ total quantity | Weighted average |
| A cheaper item replaces part of a mixture | Removed and added quantities | Replacement method |
Core Mixture Concepts
A mixture contains two or more substances combined in definite or variable quantities. If rice costing ₹40 per kilogram is mixed with rice costing ₹60 per kilogram, the average price must lie between ₹40 and ₹60. It cannot be ₹35 or ₹65 unless another operation changes the result.
The weighted-average formula is:
Mean value = Total value of all items ÷ Total quantity
For example, mixing 3 kg at ₹40 per kg with 2 kg at ₹60 per kg gives a total cost of ₹240. The total quantity is 5 kg, so the average price is ₹48 per kg. This approach is particularly reliable when the quantities are already provided.
The same principle applies to Australian supermarket calculations. If one brand of coffee costs $12 per kilogram and another costs $20, a blended pack priced at $15 must contain more of the cheaper coffee. The average price gives an immediate check on whether your answer is sensible.
Alligation Rule And Ratio
When two items are mixed to obtain a mean value, arrange the values like this:
Lower value — Mean value — Higher value
The quantity ratio is:
Quantity of lower-priced item : Quantity of higher-priced item
= Higher value − Mean value : Mean value − Lower value
Suppose tea costing ₹80 per kg is mixed with tea costing ₹120 per kg to obtain a blend costing ₹95 per kg. The ratio is:
(120 − 95) : (95 − 80) = 25 : 15 = 5 : 3
Therefore, 5 parts of the cheaper tea are mixed with 3 parts of the dearer tea. For a total of 24 kg, one part equals 3 kg, so the quantities are 15 kg and 9 kg.
The same procedure works for alcohol and water, salt solutions, alloy composition and percentage-based questions. Practise with the daily aptitude quiz to improve speed under timed conditions.
Concentration And Replacement Problems
In concentration questions, treat pure substance as 100% and water as 0%. If a solution contains 30% acid and another contains 60% acid, their mixture must have a concentration between 30% and 60%. To obtain 40%, the alligation ratio is:
60 − 40 : 40 − 30 = 20 : 10 = 2 : 1
Thus, the weaker solution and stronger solution are mixed in the ratio 2:1. This avoids unnecessary decimal calculations.
Replacement questions require a different sequence. If a container holds 40 litres of milk and 8 litres are removed and replaced with water, the fraction of milk remaining is 32/40, or 4/5. If the operation is repeated, the remaining milk is:
Initial quantity × (1 − removed quantity ÷ total quantity)ⁿ
Here, after two replacements, milk remaining is 40 × (4/5)² = 25.6 litres. Keep the replacement fraction unchanged only when the same volume is removed each time.
Students studying away from home can use short revision sessions and calm study resources between longer practice blocks, especially when balancing exam preparation with work or university schedules.
Exam Shortcuts And Error Checks
Before applying a formula, identify the two values being combined and the final value. If the mean is closer to the lower value, the lower-priced or weaker component must be present in the larger quantity. This mental check catches many reversed ratios.
Convert units before calculating. Do not combine millilitres with litres, grams with kilograms, or cents with dollars without conversion. Australian grocery labels often use kilograms and litres, while examination questions may use grams and millilitres. The ratio remains valid only when both quantities use the same unit.
For price questions, calculate total cost after finding the ratio. If the ratio is 5:3 and the total quantity is 32 kg, the total parts are 8, so each part is 4 kg. The quantities are 20 kg and 12 kg. A quick weighted-average check confirms the result.
Practice Strategy For Competitive Exams
A strong preparation routine should move from direct ratio questions to mixed problems involving percentages, replacement and profit. Begin with untimed questions to understand the structure, then use short timed sets. Banking and SSC examinations often provide limited time, so recognising an alligation pattern can save several calculation steps.
Use realistic data to build confidence: milk prices in Sydney, coffee blends from a Melbourne café, fruit sold at a Brisbane market, or commodity values connected with Perth’s mining economy. These examples make it easier to estimate answers and notice impossible results.
Recommended practice habits include:
- Memorise the alligation arrangement and write it before calculating.
- Solve at least five questions involving prices or weighted averages.
- Practise concentration problems using 0% and 100% endpoints.
- Revise replacement questions separately from ordinary mixtures.
- Check every answer against the expected range of the final value.
- Record repeated errors in a compact formula notebook.
Current affairs and exam updates can support a broader preparation schedule through currentaffairs4examz.com, where quizzes, study materials and examination resources are organised for competitive-exam learners.
Make mixture and alligation part of your weekly quantitative aptitude practice rather than leaving it for final revision. Start with ratio fundamentals, add timed concentration and replacement sets, and review each incorrect answer until the method becomes automatic.