Posted by: Kunal | February 11, 2008

Maths Dose II

Let us move on to Alligation and Removal of mixtures by equal amount.


When different quantities of same or different types and of different values are mixed together to produce a mixture of mean value. The only thing that should be taken into account while dealing with such problems is that the units of the two quantities should be same.

Sometimes the questions pertaining to some other topics can easily be solved using this concept.

Let us take an example.

Example. A merchant has 1000kg of sugar,part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 18% profit is: (NUJS-2006)

Solution. The above given question can be solved by forming a linear equation and by using alligation too. To solve it using alligation, first of all you need to check whether the quantities given (8%, 18% and 14%) are in same units. Here, they are in the same units profit percentage(%).



3x = 2000 –2x

5x = 2000

x = 400

Hence, the quantity sold at 18% profit is 1000 – 400 = 600 kg.

Let us take another example having unequal units.

Example. A man has 60 articles. He sells certain number of articles at a profit of 12% and the rest of the articles at the loss of 8%. If he makes a profit of 11% on the whole, then the number of articles sold at a loss of 8% is:

Solution. Now the quantities given (12% profit, 8% loss and 11% profit) aren’t in the same units. Hence, we can either change all the quantities given in profit into loss or vice-versa. This would be done simple by putting 8% loss as (-8)% profit.

Removal by equal amount

Consider of vessel containing only type X of ‘a’ unit. From this ‘b’ unit is taken out and replaced by an equal amount of type Y. This process is repeated ‘n’ times, then, after ‘n’ operations.


Let us have an example !!

Example. A container contains 80L of milk. From this container 8L of milk was taken out and replaced by water. This process was repeated once more. How much milk does the container have now?

Solution. Using the formula discussed above

Amount of milk left =4.gif



  1. sir,
    the remedial math classes are reslly helpful but could you give me list of math chapters we will be tested on

  2. hey its mostly class 10 basics like ratio, speed, time and work, geometry, sets and venn diagrams, linear equations,…its not as easy though….some of then are pretty difficult….

  3. oh thank you so much!

  4. dis r really helpfu

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