Quantitative Aptitude > Averages, Mixtures and Alligations
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The average is ≥ the smallest of
The average is ≤ the greater of
The Sum of deviation of each element β with respect to AM is equal to zero i.e
Rules of allegation
A shopkeeper mixes two verities of sugar costing Rs 25/Kg and Rs 20/Kg in a certain ratio such that the cost of the mixture is Rs 23/Kg then find the ratio in which the 2 types of sugar were mixed ?
Let the ratio in which sugar of rs 25/Kg and Rs 20/Kg be p:q then total cost of mixture =
Solving for p and q we get
This is the allegation rule.
Formally stated it states the ratio of dean quantity and the cheap quantity is equal to the ratio of the difference of the mean price and the cheaper price and the difference of the dean price and the mean
price symbolically where cp- cheaper price
Mp – mean price, Dp – Dean price
When we mix two or more then 2pure substance , we get what is known as a mixture.
Mixture of Mixtures :- If we mix two mixtures which have components say A and B in the final mixture is given by
The weight of first and second mixture respectively.
A special problem on mixtures
If a contains 'x' liter of liquid 'x' and if 'y' liters is taken out and replaced by 'y' liters of liquid 'z' and if the above step is repeated with the mixture so obtained that is x liter of mixture replaced with y liter of liquid 'z' then if the above operation is repeated 'n' times then
Note: The final volume of mixture remains contents and is same as initial volume same as initial of liquid X
The average age of 10students in a class is increased by 2 year when two students aged 12 year and 14 year are replaced by 2girls . Find the average age of the two girls.
Let the sum of the ages of the 2girls be y years, also sum of the ages of the 2 students who have replaced = 26 years average age of group has gone up by 2 years that means the increase in total age of the 10 students is 20 years this increase is due to the age of the 2 girls hence y – 26 = 20 , y= 4b therefore average age of the 2 girls
There are 60 students in a class . There students are divided into there groups A,B and c of 15, 20 an 25 students each . These groups A and C are combined to form group D.What is the average weight of the students in group D?
(1). More then the average weight of A
(2). More then the average weight of C
(3)Less then the average weight of C
(4) Cannot be determined.
Number of students in group D is more then number of students in group A or group C. But there is no information about the weight of students in group A or group C. Hence answer is (4)
Note : As a group D has students form group C whichever group has higher average weight , the average weight of group D will be that group s average weight
If one student from group A is shifted group B, which of the following will be true?
(1) The average weight of all the four groups is same .
(2) The average weight of both the groups decrease.
(3) The average weight of the clear remains same
(4) Cannot to be determined.
Shifting students form groups A to group b , the total number of students in the clean remains same , hence
(3)is the correct answer.
If all the students of the class have the same weight , then which of the following is not true?
(1) The average weight of all the four groups is same.
(2) The total weight of A and C is twice the total weight of B.
(3) The average weight of D is greater then the average weight of A.
(4)The average weight of all the groups remains the same even if a number of students are shifted from one group to another
Weight of each students is same is same therefore average weight of clean is same as average weight of group A,B,C and D.
Hence (3) cannot be true.
Hence option (3) is correct answer.