## Example

**Example 1:**

The average of five numbers is 29, if one number is exclude the average becomes 27. what is the exclude number ?

**Answer :**

let the exclude number is

= ( 29 x 5 ) – ( 27 x 4 )

= 145 – 108

= 37.

The exclude number 37.

**Example 2:**

What would be the average of first 20 natural numbers ?

**Answer :**

Sum of first n natural numbers = n ( n + 1 ) /2

So, we can find easily average of first 20 natural numbers 20 x 21 / 2 = 210

So, then Required average is = 210 / 20 = 10.5.

**Example 3:**

What would be the average of first 20 multiplies of 5.

**Answer:**

Required average = 5 ( 1 + 2 + 3 +……………….. + 20) /20

= ( 5 x 20 x 21 / 20 x 2) = 2100 / 40 = 52.5.

So the Required average is 52.5.

**Example 4 :**

The average marks of 13 students is 40, the first six students is 30 and that of the last six students is 32. Find the value of the 7th number.

**Answer :**

**Shortcut tricks :**

7th student marks number = Total of 13 students result – ( Total of first six students + Total of last six students results )

= 13 x 40 – ( 6 x 30 + 6 x 32 )

= 520 – 180 + 192

= 148.

**Example 5**

In a college, 16 girls has the average age is 18 years and 14 boys has the average age 17 years. What would be the average age of entire college ?

**Answer:** 16 girls has the average age is 18 years ( 16 x 18 ) =** 288**

4 boys has the average age 17 years ( 14 x 17 ) = **238**

Average age is = 288 + 238 / 30 = 526 / 30 =** 17.54 years**