MATHS TRICKS: AVERAGES
Maths Tricks : To find out the averages we use the below given formaula
Average of ‘n’ numbers = (Sum of the numbers) / n
Eg: Average of 40, 60, 25, 75 = (40+60+25+75)/4 = 200/4 = 50
This is known to us all..
In competitive exams like Kerala PSC, state PSC, UPSC, SSC, Banks etc..,., the question asked in averages is as follows (these are just a few examples….)

CLASSROOM/
When teachers age added,subtracted what is new average or
If teachers age added,subtracted what will be the change in average .. or
If a new boy comes, goes then what will be change in average or find the age of new boy etc..

MARKS
Increase or decrease in average when marks of a new student added or vice versa

CRICKETER and INNINGS
Increase or decrease in average score of a batsman, or individual score of a cricketer when we are given averages

LET US LEARN THROUGH EXAMPLES……
Q) The average age of 30 students in a class is 10. When teachers age is added the average age becomes 11. Find out the age of the teacher?
Solution)

CONVENTIONAL METHOD TO SOLVE AVERAGES
Total number of students = 30
Average age of students  = 10
Therefore the sum of ages of all 30 students = 30 x 10 = 300
When teachers age is added the total number becomes = 30 + 1 = 31
The new average = 11
Therefore the sum of ages of students and the teacher = 31 x 11 = 341
Teachers age = (Sum of ages of teacher + students) – (Sum of ages of students)
= 341- 300
= 41

VERY SIMPLE METHOD – USE YOUR COMMONSENSE:
Let us assume that the teachers age was also 10. In such case the average of all 31 people ( 30 students + 1 teacher) remains same which is 10.
But this is not the case. On arrival of teacher the average has increased by 1. So 1 has been added to all the 31 people of the class.
It means teachers age should be more than 10. How much more ? It is 31 more …
10 + 31 = 41

FORMULA METHOD
TEACHERS AGE = NEW AVERAGE + (NUMBER OF STUDENTS X DIFFERENCE OF AVERAGES)
In above case
TEACHERS AGE = 11 + ( 30 X 1) = 11+ 30 = 41

GENERAL FORMULA
 

NEW PERSON’S AGE OR WEIGHT = NEW AVERAGE + ( NUMBER OF PEOPLE BEFORE NEW PERSON CAME X DIFFERENCE BETWEEN THE NEW AND OLD AVERAGES)
TYPE II
Q) The average  marks obtained by 10 students in an exam is 55. When a boy who scored 65 marks left the class and another one joined the average reduced by 3. What was the marks of new boy?
Solution)
CONVENTIONAL METHOD
Average marks of 10 students = 55
Total marks = 55 x 10 = 550
Marks of 9 student after boy scoring 65 left = 550-65 = 485
New average for 10 students = 55 – 3 = 52
Total marks of 10 students now = 52 x 10 = 520
Therefore the marks of new boy = 520 – 485 = 35
COMMONSENSE
If the boy who came also scored 65 then no problem at all, the average would have remained same that is 55. But the average reduced by 3. So from each person he reduced 3.
Total persons  are 10
So total marks he reduced is 10 x 3 = 30
So from 65 we can reduce this 30. We get 65-30= 35
FORMULA METHOD
NEW PERSON’S AGE/WEIGHT/MARKS = AGE/WEIGHT/MARKS OF THE PERSON WHO LEFT + (TOTAL PERSONS  X  DIFFERENCE IN AGE/MARKS/WEIGHT)
NEW PERSON’S MARKS = 65 + (10 X -3) = 65 -30 = 35