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Quantitative aptitude for competitive exams –  MIXTURE AND ALLIGATION Part 2

Quantitative aptitude for competitive exams -  MIXTURE AND ALLIGATION Part 2:SUCCESSIVE REPLACEMENT

Quantitative aptitude for competitive exams –  MIXTURE AND ALLIGATION Part 2:


Consider an example to understand the concept of successive replacement.

If a vessel has x litres of milk and y litre of milk is removed from it and replaced with y litres of water the milk left in the vessel after the replacement is (x-y) litres and the total milk water solution available in the vessel is again x litres (x – y +y). so, after the replacement the proportion of milk in the milk water solution will be equal to:

Some examples:-

  1. From a solution containing milk and water in the ratio 3 : 4, 10 L is removed and replaced by water. If the resultant solution contains milk and water in the ratio 1 : 2 then what was the amount of the original solution?
    Here also we are replacing with water.  So FC and IC must be milk concentrations.
    Initial concentration of the milk = 3/7
    Final concentration of the milk = 1/3
    Applying formula
  2. 10% of a solution of milk and water is removed and then replaced with the same amount of water. If the resulting ratio of milk and water is 2 : 3, find the ratio of milk and water in the original solution.
    Applying formula:
    Here 2/5 is the milk concentration.


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  1. A beaker had 20 L of the alcohol-glycerol mixture in the ratio 4 : 1 by volume. In the first round, 4 L of the mixture is removed and replaced with glycerol. In the second round, 5 L of the resultant solution is removed and replaced with glycerol. Finally, 10 L of the resultant mixture is removed and replaced with glycerol. What is the final quantity of glycerol in the mixture
    Here we are replacing the mixture with glycerol.  So we have to take Alcohol concentrations for IC and FC.
    Initial concentration of alcohol is 4/5 = 80%
    Applying the formula for the first replacement:
    Here FC1 is the concentration after first replacement.
    Second replacement:
    Third Replacement:
    Now substituting the FC1 and FC2 in FC3 we get




  1. In a mixture of 80 L, milk and water are in the ratio 7:3. If 24 L of this mixture is replaced by 16 L if milk, find the final ratio of milk and water.
    Final volume of the mixture = 80 – 24 + 16 = 72
    Replacement quantity = 16
    Applying formula,
    So Milk and Water after replacement = 23 : 7

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March 19, 2018

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