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### Math Short Cut Tricks of SIMPLE AVERAGE SIMPLE INTEREST QUESTIONS -cutoffmarksresults.in

It is found that at least 2-3 questions are given to calculate AVERAGE based questions in SSC IBPS or other exam format. These questions are very easy to solve by using SIMPLE TRICKS in 2-3 Seconds after reading statement of question.

These FASTEST AVERAGE TRICKS helps in getting CUT-OFF score in exams. Use these tricks to solve NUMERICAL ABILIY section of SSC IBPS or other any other competitive exam.

FASTEST AVERAGE TRICKS are described as follows:
1.      AVERAGE = Sum of numbers / Total numbers
2.      If the AVERAGE of n number is m, then SUM of n numbers = mn
3.      In case of Age calculation questions, if AVERAGE of age of n persons is x before (ago) m years, then the SUM of age of n persons = n(x + m) to get present age of the group.
4.      AVERAGE = Sum of First & Last number / 2
5.      AVERAGE = Sum of Middle Terms / 2
6.      AVERAGE of Multiple of Any number = Sum of First & Last Number / 2
7.      AVERAGE of first n natural numbers = (n+1) / 2
8.      AVERAGE of first n consecutive n even numbers = (n + 1)
9.      AVERAGE of first n consecutive n odd numbers = n
10.  AVERAGE of square of first n natural numbers = [n(n+1)(2n+1)] / 6
11.  AVERAGE of cubes of first n natural numbers = [n(n+1) / 2]2
12.  SUM of 1-100 natural numbers = n (n-1) / 2
13.  SUM of First n ODD numbers = n2
14.  Geometric Mean (G. M.) of any numbers x, y, z = 3x.y.z
15.  Harmonic Mean (H. M.) of any numbers x, y, z = 1 / [1/3(1/x+1/y+1/z)]. Here 3 is the total number of which H. M. is to be calculated which can be changed if more than 3 numbers are used to calculate H. M. say if 4 numbers then it will become 4 & 5 for 5 and so-on.
16.  If any person covers some distance in two parts with two different speeds. If he covers first part at a speed of S1 km/hr and second part at a distance of S2 km/hr, then AVERAGE speed during to cover the complete distance  = 2 S1 S2 /  (S1 + S2)
17.  In case if the same person covers the whole journey in three different parts with different speeds S1 , S2 and S3 then AVERAGE speed = 3 S1 S2 S3 / (S1 S2 + S2 S3 + S3 S1)
18.  If AVERAGE of any n persons/items is increased by x then the increased AVERAGE = nx

Question 1:
The average age of 10 persons in a committee is increased by 1 year. When two men age of 42 years and 38 years are replaced by two women. Find the average age of these women.

Solution:
By using TRICK 18 (above),
The Total average age of n=10 persons increase age of m=1 year = 10x1 = 10 years.
Then Total age of two men go out from the group = 42 + 38 = 80 years
Total age of two women enters into group = 80 + 10 = 90
Then average age of these women = 90 / 2 = 45years each

Question 2:
The average age of husband and wife was 23 years when they got married 5 years ago. The age of husband, wife and children who was born during the interval is 20years now. How old is child now.

Solution:
By using TRICK 3 (above)
5 years Ago average age of Husband + Wife = 23 years
Present Average age of Husband + Wife = 23+5 = 28 years
Sum of Present age of Husband + Wife = 28 x 2 = 56 year
Similarly Sum of Present age of Husband + Wife + Child = 20 x 3 = 60.
Thus the age of Child
= (Sum of Present age of Husband + Wife + Child) - Sum of Present age of Husband + Wife)
= 60-56 = 4 years