Practice Questions
Concept Explanation
Percentage concentration expresses parts of solute per 100 parts of solution. It links directly to mixture and alligation when prices represent concentration values.
Key Formulas
- Percentage concentration = (solute / total solution) × 100
- Alligation applies: mix p1% and p2% to get pm%
- Ratio = (p2 − pm) : (pm − p1)
Example
Mix 20% and 50% solutions to get 35%. Ratio = (50 − 35) : (35 − 20) = 15 : 15 = 1 : 1.
Common Trap
Percentage is of total solution, not of solvent alone.
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Q1 EasyMix 20% and 50% solutions to get 35%. The ratio of 20% solution to 50% solution is:ExplanationAlligation: (50 − 35) : (35 − 20) = 15 : 15 = 1 : 1. Hence the answer is 1 : 1.
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Q2 Easy10% and 30% solutions mixed equally by volume. Final concentration is:ExplanationEqual volumes: mean = (10 + 30) / 2 = 20%. Hence the answer is 20%.
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Q3 Easy12% and 28% for 20%. Ratio lower : higher is:ExplanationAlligation: (28 − 20) : (20 − 12) = 8 : 8 = 1 : 1. Hence the answer is 1 : 1.
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Q4 MediumSpirit and water are in the ratio 4 : 3. On adding 6 litres of water the ratio becomes 4 : 5. The quantity of spirit in the mixture is:ExplanationLet spirit = 4k and water = 3k. After adding 6 L water: 4k / (3k + 6) = 4 / 5. Cross-multiply: 20k = 12k + 24 ⇒ 8k = 24 ⇒ k = 3. Spirit = 4 × 3 = 12 L. Hence the answer is 12 L.
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Q5 Medium40 L of 15% solution and 60 L of 25% solution. Final concentration is:ExplanationSolute = 0.15 × 40 + 0.25 × 60 = 6 + 15 = 21 L in 100 L = 21%. Hence the answer is 21%.
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Q6 Medium5% and 35% solutions for a 20% mixture. Ratio lower : higher is:ExplanationAlligation: (35 − 20) : (20 − 5) = 15 : 15 = 1 : 1. Hence the answer is 1 : 1.
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Q7 MediumA 25% sugar solution is diluted with water to 20%. If the original volume was 40 L, water added is:ExplanationSugar = 0.25 × 40 = 10 L. After dilution: 10 / (40 + x) = 0.20 ⇒ 10 = 8 + 0.2x ⇒ x = 10 L. Hence the answer is 10 L.
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Q8 Medium18% and 42% for 30%. Ratio lower : higher is:ExplanationAlligation: (42 − 30) : (30 − 18) = 12 : 12 = 1 : 1. Hence the answer is 1 : 1.
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Q9 Medium24 L of 10% and 36 L of 30%. Final concentration is:ExplanationSolute = 0.10 × 24 + 0.30 × 36 = 2.4 + 10.8 = 13.2 L in 60 L = 22%. Hence the answer is 22%.
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Q10 HardTwo alloys of copper and tin are in the ratios 5 : 2 and 3 : 4. In what ratio should they be mixed to get an alloy with copper : tin = 4 : 3?ExplanationCopper fractions: first = 5/7, second = 3/7, target = 4/7. Alligation: quantity of first : second = (4/7 − 3/7) : (5/7 − 4/7) = (1/7) : (1/7) = 1 : 1. Hence the answer is 1 : 1.
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Q11 HardIn 80 L of a 30% mixture made from 20% and 40% solutions, the volume of the 40% solution is:ExplanationAlligation for 20% and 40% to get 30%: ratio = 1 : 1. Volume of 40% solution = 80 / 2 = 40 L. Hence the answer is 40 L.
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Q12 HardMilk and water in a mixture are 75% and 25%. How much water must be added to 40 L of this mixture so that milk becomes 60%?ExplanationMilk = 0.75 × 40 = 30 L (unchanged). Need 30 / (40 + x) = 0.60 ⇒ 30 = 24 + 0.6x ⇒ 0.6x = 6 ⇒ x = 10 L. Hence the answer is 10 L.
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Q13 HardWhich pair gives 25% when mixed 1 : 1 by volume?ExplanationFor a 1 : 1 mix, mean = (p1 + p2) / 2 = 25 ⇒ p1 + p2 = 50. Option B: 15 + 35 = 50. A gives 20%, C gives 30%, D gives 22.5%. Hence the answer is B.
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Q14 Hard8% and 32% for 20%. Ratio lower : higher is:ExplanationAlligation: (32 − 20) : (20 − 8) = 12 : 12 = 1 : 1. Hence the answer is 1 : 1.
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DS1 Medium
In a campus drill, find the quantity of spirit. What is the quantity of spirit?
Statement ISpirit : water = 4 : 3 initially, and after adding 6 L water the ratio becomes 4 : 5.
Statement IIOnly the final ratio 4 : 5 after adding water is known.
ExplanationStatement I alone: 4k / (3k + 6) = 4/5 ⇒ k = 3 ⇒ spirit = 12 L. Statement II alone is insufficient. Statement I alone is sufficient. Answer: A. -
DS2 Medium
Is the final concentration 21%?
Statement I40 L of 15% and 60 L of 25% are mixed.
Statement II30 L of 8% and 70 L of 18% are mixed.
ExplanationStatement I: solute = 6 + 15 = 21 in 100 L = 21%, so Yes. Statement II: solute = 2.4 + 12.6 = 15 in 100 L = 15%, so No. Statement I alone answers the question. Answer: A.
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DS3 Hard
What is the ratio of the alloys?
Statement IAlloys have Cu : Sn = 5 : 2 and 3 : 4, and the target mixture is Cu : Sn = 4 : 3.
Statement IIOnly the target copper fraction 4/7 is known.
ExplanationStatement I alone: alligation on copper fractions 5/7 and 3/7 for 4/7 gives alloy ratio 1 : 1. Statement II alone is insufficient. Statement I alone is sufficient. Answer: A. -
DS4 Hard
How much of the 40% solution is in an 80 L mixture at 30%?
Statement IThe mixture is prepared using only 20% and 40% solutions.
Statement IINo information about the component concentrations is given.
ExplanationFrom the stem, total = 80 L and mean = 30%. Statement I: components are 20% and 40%, so alligation ratio = 1 : 1 and volume of 40% solution = 40 L. Statement II alone is useless. Statement I alone is sufficient. Answer: A.