# 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 n
^{2}

## 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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