# Tips And Tricks And Shortcuts for Averages

## Tips, Tricks and Shortcuts for Averages in Aptitude

Here, We are discussing the best approach to understand the questions from averages and also using Tips and Tricks for Averages we can avoid unwanted calculation.

### 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 = $\mathbf{\frac{X_{1}+X_{2}+X_{3}+X_{4}+…..X_{n}}{n}}$

OR

Average = $\frac{\text{Sum of Observations}}{\text{Total Number of Observations}}$

Trick 1 : 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.

Trick 2 : 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.

Trick 3 : 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

Trick 4 : 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)

Trick 5 :

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).

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

• Average  of ‘n’ consecutive Natural Numbers =
$\mathbf{\frac{n+1}{2}}$
• Average of the square of consecutive n natural numbers =
$\mathbf{\frac{(n+1)(2n+1)}{6}}$
• Average of cubes of consecutive n natural numbers =
$\mathbf{\frac{n\times (n+1)^{2}}{4}}$
• Average of n consecutive even numbers = (n+1)
• Average of consecutive even numbers till n =
$\mathbf{\frac{n}{2}+1}$
• Average of n consecutive odd numbers = n
• Average of consecutive odd numbers till n =
$\mathbf{\frac{n+1}{2}}$
• Sum of 1st n even consecutive natural numbers is =  n(n + 1)
• Sum of 1st n odd consecutive natural numbers is = $\mathbf{n^{2}}$

### Type 1: Tips to Solve Problems on Weights and Ages Average

Question 1: When a new man joins a group of 5 people after Replacing a man, their average age increases by 2 kg. If he replaces a man weighing 40 kg, how much does he weigh?

Solution :  Increased weight = (5 x 2) = 10

Weight of the new man = (40 +10) = 50 kg

Question 2: 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 year’s

Sum of their ages excluding the youngest monkey = 80 – 8 = 72 year’s

The average age of the remaining monkey = $\frac{72}{3} = 24$ years

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

Question 1 : If the Marks of Each student is 70 and it is increased by 20, then the average of the class will be

Solution:  Average of the class = 70+20 = 90

Question 2: 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 x 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 : A bus Travels from Place A to Place B.During this it covers 150 km in 3 hours and 350  km in 2 hours.find the average speed of the bus.

Solution : Average speed = $\frac{\text{Total distance Travelled}}{\text{Total Time Taken}} = \frac{150+350}{3+2} = 100$ km/hr

Question 2 : The average speed of a train without stopping at any stoppages is 48 km/h, and average speed when the train stops at different stoppages is 40 km/h. How many minutes in an hour does the train stop on an average?

Solution: The average speed of a train without stoppages = 48 km/h

With stoppages, the average speed reduces by (48-40) = 8 kms

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

= $\frac{8}{48}\times 60$ minutes

= 10 minutes

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

Question 1 : The average of N consecutive natural numbers is 7. Find out the value of n.

Solution: Average of n consecutive natural numbers is = $\frac{(n+1)}{2}$

7 = $\frac{(n+1)}{2}$

n+1= 14

n = 13

Question 2: 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 = $\frac{(n+1)(2n+1)}{6}$

20 = $\frac{(n+1)(2n+1)}{6}$

120 = 8 x 15

120 = (7+1)(2×7+1)

n =7

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### 6 comments on “Tips And Tricks And Shortcuts for Averages”

• Harshitha

Could anyone explain type 4 answer

• HelpPrepInsta

Hello Harshita ,
“The average of squares of first n natural numbers = (n+1)(2n+1)/6”

This is the formula of Arithmetic Progression .

Warm Rgards ,
PrepInsta Team

• srinivas

In type2 question why we have to Multiplying (1) by 12 and subtracting from (2)

• Vaibhav Jain

In this type of questions we form 2 quadratic equations and try to solve them for calculating the desired answer. So in the process of solving those quadratic equations, we need to make atleast one of the variable equal in both the equation, that is the reason why we multiplied eq 1 by 12

• Premkumar

Sir how do we get 48 in type 3 question1

• Ashish Mishra

Hi Prepkumar,
It is already given in the question that when train move by stopping than it speed is 48kmph. And we need to find its average stoppage time.
Thank You