**What is Average?**

The result obtained by adding several quantities together and then dividing this total by the number of quantities is called Average.

The main term of average is **an equal distribution of value** among all which may distribute persons or things. We obtain the average of a number using a formula that is the sum of observations divided by the Number of observations.

Here are average based some facts, formulas and shortcut tricks examples. Given below are some more example of practising.

**Formula:**

- Average: = (Sum of observations / Number of observations).

**Find the Average Speed**

- If a person travels a distance at a speed of x km/hr and the same distance at a speed of y km/hr then the average speed during the whole journey is given by 2xy/(x+y)
- If a person covers A km at x km/hr and B km at y km/hr and C km at z km/hr, then the average speed in covering the whole distance is- 3xyz/(xy + yz + zx)
**When a person leaves the group and another person joins the group in place of that person then-**

- If the average age is increased,
**Age of new person**= Age of separated person + (Increase in average × total number of persons) **If the average age is decreased,**= Age of separated person - (Decrease in average × total number of persons)

Age of new person

**When a person joins the group-****In case of an increase in average**

- Age of new member = Previous average + (Increase in average × Number of members including new member)

**In case of a decrease in average**

- Age of new member = Previous average - (Decrease in average × Number of members including new member)

**In the Arithmetic Progression, there are two cases when the number of terms is odd and second one is when the number of terms is even.**

- So when the number of terms is odd the average will be the middle term.
- when the number of terms is even then the average will be the average of two middle terms.

**Question 1. **The average of 8 numbers is 20. The average of first two numbers is 15.5 and the average of next three number is If the 6^{th} number is 4 and 7 less by the 7^{th} and the 8^{th} numbers respectively then what will be the 8^{th} number?

(1) 25

(2) 22

(3) 35

(4) 30

Solution:

**Short Trick: **

Sum of all = 160

Sum of first 5 = 95 coming from

sum of last 3 = 65

x + x + 4 + x + 7 = 65

** 18 + 22 + 25**

**Answer: 1**

**Question ****2: **The average temperature from Monday to Wednesday is 37^{0}C while the average temperature from Tuesday to Thursday is 34^{0}C. The temperature of Thursday is times to that of Monday. Find the temperature of Thursday?

(1) 36^{0}C

(2) 33^{0}C

(3) 37^{0}C

(4) 34^{0}C

**Solution:**

**Short Trick: **

Mon + Tues + Wed = 111

Tues + Wed + Thurs + 102 (diff. = 9)

**Question ****3: ** Of the three numbers whose average is 60, the first is one-fourth of the sum of the others. The first number is

(1) 30

(2) 36

(3) 42

(4) 45

**Solution:**

x + y + z = 180 …………(i)

Putting the value of y + z in

Equation …………….(i) x + 4x = 180

5x = 180 x = 36

Question 4: The average of marks obtained by 120 candidates in a certain examination is 35. If the average marks of passed candidates is 39 and that of the failed candidates is 15, what is the number of candidates who passed the examination?

(1) 100

(2) 120

(3) 140

(4) 160

**Solution:**

Let the number of passed candidates be x

Then total marks = 120 x 35 = 39x + (120 – x) x 15

Or, 4200 = 39x + 1800 – 15x

Or, 24x = 2400

x = 100

Number of passed candidates = 100

**Short Trick:**

Pass Fail

39 15

\ /

35

/ \

20 4

** 5 : 1**

Hence, total number of passed candidates

Question 5:** **The average weight of 8 persons is increased by 2.5 kg when one of them who weight 56 kg is replaced by a new man. The weight of the new man is

(1) 73 kg

(2) 72 kg

(3) 76 kg

(4) 80 kg

**Solution: **

Aw_{2} – AW_{1} = 2.5

Total weight_{1} – Total weight_{2 } = 20.0 kgs

This difference is because of the new man.

Hence the weight of the new man = 56 + 20 = 76 kgs.

**Short Trick: **

56 + 8 x 2.5

= 76 kgs

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