#### 1.

A person travels from A to B at a speed of x km./h and returns B to A at a speed of y km./h, then his average speed:

__Example-__
If Reeta travels from Goa to Delhi at a speed of 105 km./h and from Delhi to Goa at a speed of 120 km./h. Find his average speed.

__Solution:__

#### 2.

If a person travels three equal distance at a speed of X km./h, Y km/h and Z km/h respectively, then average speed:

__Example.__
If Mahima travels three equal distance at a speed of 120 km/h, 125 km/h and 140 km/h respectively. Find her Average speed.

__Solution:__

#### 3.

If the distance ‘A’ is covered with a speed of x km/h, distance ‘B’ is covered with a speed of y km/h and distance ‘C’ is covered with a speed of z km/h, then average speed:

__Example-__
If the distance 75 km is covered with a speed of 25 km/h, distance 40 km is covered with a speed of 20 km/h and distance 60 is covered with a speed of 20 km/h. Find the average speed.

__Solution:__
The average of a items is x and the average of b item is y, then total average of (a+b) is

__Example-__
If the average salary of 7 month is 25200 and the average salary of 5 month is 24000. Find the average salary of 12 months.

__Solution:__

####

5.

There are total ‘x’ members and their total average age is ‘a’ years. Then a new member joins and the new average age of the members become ‘n’, then the age of new member that joins will be

= [n+x(n-a)] years

= [n+x(n-a)] years

__Example-__
If the average age of 15 students in a class is 20 and a teacher joins the class then their average age increase by 1. What will be the age of teacher?

After joining the teacher new average= 20+1 = 21 years

The age of teacher = 21+15(21-20)

=21+15

=36 years

__Solution:__After joining the teacher new average= 20+1 = 21 years

The age of teacher = 21+15(21-20)

=21+15

=36 years

#### 6.

There are total ‘x’ members and their total average age is ‘a’ years. Then a member leaves and the new average age of the members become ‘n’, then the age of new member that joins will be

= [n-x(n-a)] years

= [n-x(n-a)] years

__Example__
A class of 19 children and a teacher, the average weight is 48 kg. If the weight of the teacher is excluded, then the new average weight becomes 48.5. What is the weight of the teacher?

=48.5-20(48.5-48)

=48.5-10

=38.5 years

__Solution:__=48.5-20(48.5-48)

=48.5-10

=38.5 years

## Some important points:

#### 7.

If the value of each item is increased by the same value, then their total average will also be increased by that same value.

__Example__
The Average of five numbers 55,45,65,95,85 is 69. If each number is increased by 5, then what is the new average?

New average= 69+5= 74

__Solution:__New average= 69+5= 74

#### 8.

If the value of each item is decreased by the same value, then their total average will also be decreased by that same value.

__Example-__
The Average of five numbers 55,45,65,95,85 is 69. If each number is decreased by 5, then what is the new average?

New average= 69-5= 64

__Solution:__New average= 69-5= 64

#### 9.

If the value of each item is multiplied by the same value, then their total average will also be multiplied by that same value.

__Example-__
The Average of five numbers 55,45,65,95,85 is 69. If 5 is multiplied with each number then what is the new average?

New average= 69×5= 345

__Solution:__New average= 69×5= 345

#### 10.

If the value of each item is divided by the same value, then their total average will also be divided by that same value.

__Example-__
The Average of five numbers 55,45,65,95,85 is 69. If 5 is divided from each number then what is the new average?

New average= 69/5= 13.8

__Solution:__New average= 69/5= 13.8

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