Q1
Not Answered
NATIVE
Q1. A 25 L vessel is full of milk. 15 L milk is removed and replaced with water. What is milk percentage now?
Milk left = 10 L out of 25 L. Milk % = 10/25 x 100 = 40%.
Home / General Aptitude / Mixtures
General Aptitude
Mixtures
Solve mixture and allegation-style questions on concentration, replacement, and weighted averages.
About Mixtures
Mixture and Alligation problems are a key part of quantitative aptitude tests, frequently appearing in placement exams, banking exams, and competitive screening rounds. These questions test your ability to calculate the resulting concentration or price when two or more substances are combined. Common question types include: finding the average price of a mixed commodity, calculating the ratio in which two mixtures should be combined to achieve a target concentration, solving replacement problems (removing part of a mixture and refilling), and weighted-average percentage problems. The Alligation rule provides a shortcut: if two ingredients are mixed, the ratio of their quantities equals the inverse difference of their individual prices/percentages from the mean. Below are solved mixture and alligation questions with detailed step-by-step explanations.
Key Takeaways
- Alligation rule: ratio = (higher - mean) : (mean - lower) for two-ingredient mixtures.
- Replacement problem: after n replacements, concentration = initial × (1 - fraction_replaced)^n.
- Always convert percentages to fractions for easier mental calculation in mixture problems.
Frequently Asked Questions
What is the Alligation rule?
Alligation is a shortcut to find the ratio in which two ingredients at different prices/concentrations must be mixed to obtain a mixture at a desired mean price/concentration. Ratio = (Higher value - Mean) : (Mean - Lower value). This avoids solving linear equations.
How do replacement problems work?
When a quantity is removed from a mixture and replaced with another ingredient, the concentration reduces by a factor each time. After n replacements: Final concentration = Initial concentration × (1 - Replaced/Total)^n. This is similar to compound interest in reverse.
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20 questions
~6 minutes
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Explanations included
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Q2
Not Answered
NATIVE
Q2. Mix 18 L of 30% acid solution with 7 L of 80% solution. Find final acid percentage.
Final % = (18x30+7x80)/(25) = 44%.
Q3
Not Answered
NATIVE
Q3. A 40 L vessel is full of milk. 10 L milk is removed and replaced with water. What is milk percentage now?
Milk left = 30 L out of 40 L. Milk % = 30/40 x 100 = 75%.
Q4
Not Answered
NATIVE
Q4. Mix 10 L of 40% acid solution with 15 L of 90% solution. Find final acid percentage.
Final % = (10x40+15x90)/(25) = 70%.
Q5
Not Answered
NATIVE
Q5. A 20 L vessel is full of milk. 15 L milk is removed and replaced with water. What is milk percentage now?
Milk left = 5 L out of 20 L. Milk % = 5/20 x 100 = 25%.
Q6
Not Answered
NATIVE
Q6. Mix 16 L of 20% acid solution with 16 L of 80% solution. Find final acid percentage.
Final % = (16x20+16x80)/(32) = 50%.
Q7
Not Answered
NATIVE
Q7. A 50 L vessel is full of milk. 20 L milk is removed and replaced with water. What is milk percentage now?
Milk left = 30 L out of 50 L. Milk % = 30/50 x 100 = 60%.
Q8
Not Answered
NATIVE
Q8. Mix 13 L of 50% acid solution with 13 L of 80% solution. Find final acid percentage.
Final % = (13x50+13x80)/(26) = 65%.
Q9
Not Answered
NATIVE
Q9. A 40 L vessel is full of milk. 20 L milk is removed and replaced with water. What is milk percentage now?
Milk left = 20 L out of 40 L. Milk % = 20/40 x 100 = 50%.
Q10
Not Answered
NATIVE
Q10. A shopkeeper mixes 8 kg tea at Rs. 31/kg with 8 kg tea at Rs. 127/kg. What is average cost per kg?
Average cost = (8x31+8x127)/(16) = 79.
Q11
Not Answered
NATIVE
Q11. A 20 L vessel is full of milk. 10 L milk is removed and replaced with water. What is milk percentage now?
Milk left = 10 L out of 20 L. Milk % = 10/20 x 100 = 50%.
Q12
Not Answered
NATIVE
Q12. Mix 12 L of 30% acid solution with 8 L of 90% solution. Find final acid percentage.
Final % = (12x30+8x90)/(20) = 54%.
Q13
Not Answered
NATIVE
Q13. A shopkeeper mixes 6 kg tea at Rs. 38/kg with 7 kg tea at Rs. 142/kg. What is average cost per kg?
Average cost = (6x38+7x142)/(13) = 94.
Q14
Not Answered
NATIVE
Q14. A 25 L vessel is full of milk. 10 L milk is removed and replaced with water. What is milk percentage now?
Milk left = 15 L out of 25 L. Milk % = 15/25 x 100 = 60%.
Q15
Not Answered
NATIVE
Q15. A shopkeeper mixes 8 kg tea at Rs. 76/kg with 8 kg tea at Rs. 132/kg. What is average cost per kg?
Average cost = (8x76+8x132)/(16) = 104.
Q16
Not Answered
NATIVE
Q16. A 25 L vessel is full of milk. 5 L milk is removed and replaced with water. What is milk percentage now?
Milk left = 20 L out of 25 L. Milk % = 20/25 x 100 = 80%.
Q17
Not Answered
NATIVE
Q17. Mix 15 L of 40% acid solution with 10 L of 90% solution. Find final acid percentage.
Final % = (15x40+10x90)/(25) = 60%.
Q18
Not Answered
NATIVE
Q18. A shopkeeper mixes 10 kg tea at Rs. 38/kg with 5 kg tea at Rs. 98/kg. What is average cost per kg?
Average cost = (10x38+5x98)/(15) = 58.
Q19
Not Answered
NATIVE
Q19. Mix 14 L of 20% acid solution with 6 L of 60% solution. Find final acid percentage.
Final % = (14x20+6x60)/(20) = 32%.
Q20
Not Answered
NATIVE
Q20. A shopkeeper mixes 15 kg tea at Rs. 69/kg with 15 kg tea at Rs. 145/kg. What is average cost per kg?
Average cost = (15x69+15x145)/(30) = 107.
Quiz Summary
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Mixtures Formula, shortcuts & preparation guide
Master mixtures with regular practice. Key topics include percentage calculations, profit/loss, ratio, and time-work problems. Use shortcut methods for quick calculations and practice 15-20 questions daily to build speed and accuracy. This topic frequently appears in placement aptitude rounds.
Key formulas
- Regular practice improves accuracy
Mixtures Practice Questions with Answers
Build speed and accuracy with curated mixtures practice. Each quiz includes solved explanations, timed mode, and instant correctness feedback.
How to prepare effectively for this topic?
Practice short timed sets daily, review every explanation, and track recurring mistakes for weekly revision.
Are these questions useful for placements and competitive exams?
Yes. The format mirrors common screening rounds with option-based answers and explanation-driven learning.