Practice Questions
Concept Explanation
When a fixed quantity is repeatedly removed from a vessel and replaced with impurity (e.g. water), the pure quantity decreases exponentially.
Key Formulas
- After n replacements of x out of V (starting pure): pure left = V(1 − x/V)n
- Concentration after n operations = (1 − x/V)n × 100%
- After one step: pure = V − x
Example
64 L pure milk. Remove 8 L, add 8 L water, repeat 3 times. Pure = 64 × (7/8)³ = 42.875 L.
Common Trap
Apply the power n only after the same operation is repeated n times with the same x and V.
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Q1 Easy
100 L pure: remove 10 L, add 10 L water, once. Pure left is:
ExplanationPure left = 100 × (1 − 10/100) = 90 L. -
Q2 Medium
100 L pure: 10 L replaced with water, twice. Pure left is:
ExplanationPure = 100 × (0.9)² = 81 L. -
Q3 Hard
64 L pure: 8 L replaced with water, 3 times. Pure left is:
ExplanationPure = 64 × (7/8)³ = 42.875 L. -
Q4 Easy
125 L pure: 25 L replaced once. Concentration of pure is:
ExplanationPure = 100 L in 125 L = 80%. -
Q5 Medium
50 L pure: 5 L replaced with water, twice. Pure left is:
ExplanationPure = 50 × (0.9)² = 40.5 L. -
Q6 Easy
80 L pure: 20 L replaced once. Fraction pure left is:
ExplanationPure = 60/80 = 3/4. -
Q7 Hard
27 L pure: 3 L replaced with water, 3 times. Pure left is:
ExplanationPure = 27 × (8/9)³ = 27 × 512/729 = 19.44 L.
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Q8 Easy
100 L pure: 20 L replaced once. Pure left is:
ExplanationPure = 100 × 0.8 = 80 L. -
Q9 Medium
100 L pure: 20 L replaced, twice. Pure left is:
ExplanationPure = 100 × (0.8)² = 64 L. -
Q10 Easy
Formula for pure after n replacements of x from V is:
ExplanationPure left = V(1 − x/V)^n after n identical replacements. -
Q11 Medium
40 L pure: 4 L replaced with water, 2 times. Pure left is:
ExplanationPure = 40 × (0.9)² = 32.4 L. -
Q12 Hard
1000 L pure: 100 L replaced, 3 times. Pure left is:
ExplanationPure = 1000 × (0.9)³ = 729 L. -
Q13 Hard
After 2 replacements of 1/4 from pure V, pure left is:
ExplanationPure = V × (3/4)² = 9V/16. -
Q14 Easy
60 L pure: 6 L replaced once. Water added is 6 L. Pure concentration is:
ExplanationPure = 54/60 = 90%.
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DS1 Easy
How much pure liquid remains?
Statement I100 L pure: 10 L replaced with water, twice.
Statement IIPure left is 81 L.
ExplanationEach confirms 100 × (0.9)² = 81 L. -
DS2 Hard
What is the concentration after 3 replacements?
Statement I64 L pure, 8 L replaced each time with water.
Statement IIPure left is 42.875 L in 64 L.
ExplanationStatement I alone: 64 × (7/8)³ = 42.875 L, concentration = 67.0%.
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DS3 Medium
Is less than 70% pure left?
Statement I100 L pure: 20 L replaced, twice.
Statement II50 L pure: 5 L replaced, twice.
ExplanationI: 64% pure. II: 81% pure. I alone answers Yes. -
DS4 Medium
How many replacements were done?
Statement IPure left = V(1 − x/V)^n.
Statement IIPure = 100 × (0.9)² = 81 L after identical operations.
ExplanationStatement II alone: n = 2 from (0.9)².