Practice Questions
Concept Explanation
In replacement, a fixed quantity is removed from a vessel and an equal quantity of another liquid (often water) is added. The concentration of the original liquid decreases.
Key Formulas
- After one replacement of a litres from V litres of pure liquid with water: pure left = V − a = V(1 − a/V)
- Fraction of original left after one draw = (V − a)/V
- After replacement, new concentration = old concentration × (V − a)/V
Example
100 L pure milk. Remove 20 L, add 20 L water. Pure milk left = 80 L. Concentration = 80%.
Common Trap
Replacement is not the same as simple dilution. You remove a mixture (if not pure initially), not just the solute.
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Q1 Easy
100 L pure milk: 20 L removed and 20 L water added. Milk left is:
ExplanationPure milk left = 100 − 20 = 80 L. -
Q2 Easy
After above, concentration of milk is:
Explanation80 L milk in 100 L total = 80%. -
Q3 Easy
60 L pure juice: 15 L removed, 15 L water added. Juice left is:
ExplanationJuice left = 60 − 15 = 45 L. -
Q4 Easy
80 L solution: 10 L removed and 10 L water added. Fraction of original left is:
ExplanationFraction left = (80 − 10)/80 = 7/8. -
Q5 Easy
50 L at 100% purity: remove 5 L, add 5 L water. Purity becomes:
ExplanationPure left = 45 L in 50 L = 90%. -
Q6 Medium
200 L wine: 40 L drawn off and 40 L water added. Wine left is:
ExplanationWine left = 200 − 40 = 160 L. -
Q7 Medium
120 L pure: remove 24 L, add 24 L impurity. Pure quantity left is:
ExplanationPure left = 120 − 24 = 96 L.
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Q8 Medium
Vessel has 64 L pure. Remove 8 L, add 8 L water. Milk fraction is:
ExplanationPure left = 56 L in 64 L = 56/64 = 7/8. -
Q9 Easy
40 L pure oil: 8 L removed, 8 L cheaper oil added (not water). Pure oil left is:
ExplanationPure oil removed = 8 L. Left = 40 − 8 = 32 L. -
Q10 Hard
100 L at 80% concentration: remove 20 L and add 20 L water. New concentration is:
ExplanationPure = 80 − 16 = 64 L in 100 L = 64%. -
Q11 Medium
90 L pure: remove 18 L, add 18 L water. Percentage pure left is:
ExplanationPure left = 72 L in 90 L = 80%. -
Q12 Easy
After replacing 1/5 of 100 L pure with water, pure left is:
ExplanationRemove 20 L: pure left = 80 L. -
Q13 Easy
25 L pure: remove 5 L, add 5 L water. Concentration is:
Explanation20 L pure in 25 L = 80%. -
Q14 Hard
Which leaves the most pure liquid after one replacement of 10 L from 100 L?
ExplanationReplacing with pure liquid keeps 100 L pure; water leaves 90 L pure.
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DS1 Easy
How much pure liquid remains?
Statement I100 L pure: 20 L removed and 20 L water added.
Statement IIFinal concentration is 80%.
ExplanationEach gives 80 L pure remaining. -
DS2 Easy
What is the new concentration?
Statement IInitial volume is 80 L pure.
Statement II10 L is removed and 10 L water is added.
ExplanationPure left = 70 L in 80 L = 87.5%.
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DS3 Medium
Is less than 70% pure left?
Statement I60 L pure: 20 L removed, 20 L water added.
Statement II100 L pure: 25 L removed, 25 L water added.
ExplanationI: 40/60 = 66.7% < 70%. II: 75% — not sufficient alone. -
DS4 Easy
What fraction of original remains after one replacement?
Statement IVolume is 120 L and 24 L is replaced with water.
Statement II1/5 of the contents is replaced with water.
ExplanationEach gives fraction left = (120 − 24)/120 = 4/5.