Mixture and Alligation: Replacement of Liquids

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.