Practice Questions
Concept Explanation
Mixed alligation problems combine multiple concepts: price mixtures, concentration, replacement, and ratio finding in multi-step scenarios typical of placement exams.
Key Formulas
- Alligation: cheaper/dearer = (d − m)/(m − c)
- Mean price = (C1Q1 + C2Q2)/(Q1 + Q2)
- Replacement: pure = V(1 − x/V)n
- Concentration mix: C1V1 + C2V2 = Cm(V1 + V2)
Example
Mix Rs. 30/kg and Rs. 50/kg tea for Rs. 38/kg, then add water (Rs. 0/L). Use alligation first, then dilution if needed.
Common Trap
Break multi-step problems into stages: mix first, then replace or dilute.
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Q1 Easy
Rs. 30/kg and Rs. 50/kg for Rs. 38/kg. Ratio cheaper : dearer is:
Explanation(50 − 38) : (38 − 30) = 12 : 8 = 3 : 2. -
Q2 Hard
30 kg mix costs Rs. 840 at Rs. 28/kg. Adding 10 kg water (Rs. 0/kg). New mean price per kg is:
ExplanationTotal cost unchanged at Rs. 840 for 40 kg. Mean = 840/40 = Rs. 21/kg. -
Q3 Hard
100 L pure milk, 20 L removed and 20 L water added, twice. Milk left is:
ExplanationPure = 100 × (0.8)² = 64 L. -
Q4 Medium
Mix 20% and 50% acid for 35%, then dilute with water to 17.5%. Water added equals original volume?
Explanation35% to 17.5% halves concentration — volume doubles. Water added = original volume. -
Q5 Medium
Rs. 24/kg and Rs. 36/kg for Rs. 30/kg. In 60 kg mix, cheaper quantity is:
ExplanationRatio 1:1. Cheaper = 30 kg. -
Q6 Easy
40 L of 25% alcohol and 60 L of 15% alcohol. Final concentration is:
ExplanationSolute = 10 + 9 = 19 in 100 L = 19%. -
Q7 Easy
A dealer mixes 20 kg at Rs. 50/kg with 30 kg at Rs. 70/kg. Mean price is:
ExplanationMean = (1000 + 2100)/50 = Rs. 62/kg.
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Q8 Medium
64 L pure, 8 L replaced with water 2 times. Milk left is:
ExplanationPure = 64 × (7/8)² = 49 L. -
Q9 Hard
Rs. 15/kg and Rs. 45/kg for Rs. 27/kg. Cheaper share in 60 kg is:
ExplanationRatio cheaper : dearer = (45 − 27) : (27 − 15) = 3 : 2. Cheaper = 2/5 × 60 = 24 kg. -
Q10 Hard
Mix 10 L of 20% acid with 20 L of 40% acid, then add 20 L water. Final acid concentration is:
ExplanationSolute = 2 + 8 = 10 in 50 L total = 20%. -
Q11 Medium
A 50 kg mix at Rs. 32/kg uses Rs. 26/kg and Rs. 38/kg goods. Ratio cheaper : dearer is:
Explanation(38 − 32) : (32 − 26) = 6 : 6 = 1 : 1. -
Q12 Hard
80 L vessel: 20 L removed and 20 L water added 3 times from pure. Milk left is:
ExplanationPure = 80 × (3/4)³ = 33.75 L. -
Q13 Easy
Which problem needs alligation first?
ExplanationAlligation finds the ratio for mixing two prices to a target mean. -
Q14 Hard
Rs. 22/kg and Rs. 58/kg for Rs. 34/kg. Dearer share in 90 kg is:
ExplanationRatio = (58−34):(34−22) = 24:12 = 2:1. Dearer = 1/3 × 90 = 30 kg.
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DS1 Easy
What is the mean price of the mixture?
Statement IRs. 30/kg and Rs. 50/kg are mixed for Rs. 38/kg.
Statement II18 kg at Rs. 30/kg and 12 kg at Rs. 50/kg are mixed.
ExplanationEach gives mean = (540 + 600)/30 = Rs. 38/kg. -
DS2 Easy
How much milk remains after two replacements?
Statement I100 L pure, 20 L replaced with water each time.
Statement IIPure left is 64 L.
ExplanationEach gives 100 × (0.8)² = 64 L.
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DS3 Hard
Can the final concentration be found?
Statement I20% and 50% solutions are mixed for 35%.
Statement IIThe resulting 35% solution is diluted with equal volume of water.
ExplanationNeed both steps: 35% then halved to 17.5%. -
DS4 Medium
What is the cheaper quantity in the mix?
Statement IRs. 24/kg and Rs. 36/kg give Rs. 30/kg.
Statement IITotal mixture is 60 kg.
ExplanationNeed both: ratio 1:1, cheaper = 30 kg.