Tips And Tricks And Shortcuts on Averages

Tips and Tricks to Calculate Averages | Shortcuts in Averages:-

Find below , the best Tips and Tricks and Shortcuts on Averages apart from the basic method of solving

Basic Tips and Tricks for Averages:

Average =x1 + x2 + x3 + x4 +………… xn
n

or

Average  =Sum of Numbers
Number of Units
 

If the value of each unit in a class is increased by some value x, then the average of the class also increases by x. 

For example, if the marks obtained by of Raj and Rohit increases by 20 marks each, the average of the total marks of both also increases by 20.

 If the value of each unit in a class decreases by some value x, then the average of the class also decreases by x.

For example, if the score of Raj and Rohit in a match is decreased by 20 individually, the average score of both also decreases by 20.

The average of any number series or group is always between its smallest and the largest value.
For example- 
If the average test score of four children are 6,9,10,11 than the average of all four name respectively is 9.

When a person leaves the group, and replacement is made of that person then:

If the average age increases,

Age of new person = Age of separated person + (increase in the average × total number of persons).

If the average age decreases,

Age of new person = Age of separated person – (decrease in the average × total number of persons).

When a person joins the group,

When the average age is increased

Age of new person = Previous average + (increase in average × total members including new member).

When the average age is decreased

Age of new person = Previous average – (decrease in average × total members including new member).

Tips and Tricks and Shortcuts to Calculate average of a Series:

  • Average  of ‘n’ consequtive Natural Number
     n +1
    2
  • Average of the square of consecutive n natural numbers
 (n +1)(2n +1)
6
  • Average of cubes of consecutive n natural numbers
     n(n +1)2
    4
  • Average of n consecutive even numbers = (n+1)
  • Average of consecutive even numbers till n
     n + 1
    2
  • Average of n consecutive odd numbers = n
  • Average of consecutive odd numbers till n
     n +1
    2
  • Sum of 1st n even consecutive natural numbers is n(n + 1)
  • Sum of 1st n odd consecutive natural numbers is n2

Type 1: Tips to Solve Problems on Weights and Ages Averages

Question 1.

The average age of 4 monkeys is 20 years. The youngest monkey is eight years old. When he was born, the average age of the remaining monkeys was N years. Calculate the average age of the monkeys excluding the youngest monkey?

Solution:

The average age of monkey = 20 years.

Sum of all their ages = 20×4= 80 years

Sum of their ages excluding the youngest monkey = 80 – 8 = 72 years

The average age of the remaining monkey = 72/3  = 24 years

Type 2: Tips to Solve Problems on Average Marks and Scores

Question 1. 

The average marks of 80 students of 10th standard is 40. The average marks of students of section A is 35, and that of Section B is 60. Find the number of students in section A.

Solution:

Let the number of students in Section A and Section B be x and y.

Total number of students including Section A and Section B = 80

=> x+y = 80…(1)

Total marks obtained by entire 10th Standard = 80*40 =3200

35x+60y =3200

=> 7x+12y=640…(2)

Multiplying (1) by 12 and subtracting from (2)

we get,

x=64

Type 3: Tips to Solve Problems on Speed Distance Time Averages

Question 1. 

The average speed of a train without stopping at any stoppages is 58 km/h, and average speed when the train stops at different stoppages is 50 km/h. How many minutes in an hour does the train stop on an average?

Solution:

The average speed of a train without stoppages = 58 km/h

With stoppages, the average speed reduces by (58-50) = 8 km

Therefore, the time per hour the train stops on an average

= (8/48) × 60 minutes

= 10 minutes

Type 4: Tips and Tricks to Solve Average Problems on Numbers

Question 1. 

The average of the square of N consecutive natural numbers is 20. Find out the value of N.

Solution:

Average of square of n consecutive natural numbers is = (n+1)(2n+1)/6

20 = (n+1)(2n+1)/6

120 = 8*15

120 = (7+1)(2*7+1)

n =7

Read Also: How to solve Problem on Averages question

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