# Allegations and Mixtures Tricks basics-Problems with Solutions and Examples-put Formula and get answer-tutorial

Allegations and Mixtures types of questions are asked in most of the competitive exams and other exams. In allegations and mixtures types of questions, you are given a mixture of two or more substances or liquids and you have to do their calculations. In this types of problems, there are many shortcut methods you will see in books, but here we will suggest you that method, which you will hardly find in any book.
Suppose you are given a question like the one given below:
Q: In a 60 liters mixture of milk and water, the quantity of milk is 5 %. In how much quantity, should milk be added to this mixture so that the quantity of milk in the mixture becomes 15 % ?
Now in this question, we have to add the milk to the solution in that quantity so that the quantity of milk in the mixture get to be 15 %.
Here is a shortcut formula for this type of questions. Just follow the rule given below for this type of question and remember the formula.

Rule: In x gram mixture of milk and water, milk is p %. To make the quantity of milk in the mixture to be q %, the quantity of milk added to the mixture will be

=x{(q-p)/(100-q)}

Now let us solve the question given above as per this rule:

Here in this question:
X= 60 liters,         p= 5 %,                 q= 15 %
The quantity of milk to be added  to the mixture to make it 15 % in mixture-
=60*{(15-5)/(100-15)
=60*(10/85)
=120/17 liters     answer

Similar opposite question to the above is here. In this question the formula is slightly changed.
Rule 2: in x gram mixture of milk and water, there is p % water. To make the quantity of water to be q % , the quantity of water to be converted into steam will  be
=x{(p-q)/(100-q)}

Question based on rule 2:
In 750 gram of mixture of salt and water, there is 30 % water. How much water should be converted to steam so that water in the mixture remains 25 %.
Solution:
Here in this question,
X=750 gram,       p= 30 %,               q= 25 %
Now putting the formula given in Rule 2:
The quantity of water which should be converted to steam will be
= 750*{(30-25)/(100-25)                grams
=750*(5/75)       grams
= 50 grams

So 50 grams of water should be converted to steam to make the mixture having the quantity of water 25 % remaining.