## Average:

#### Average = Sum of Quantities/Number of Quantities

#### Average is Known as Mean

### Important Points:

1. Average of n multiples of x will be=

2. Average of consecutive first n natural numbers is=

3. Average of first n natural even numbers is= (n+1)

4. Average of natural even numbers upto n is=

5. Average of first n natural odd numbers is = n

6. Average of natural odd numbers upto n is =

7. If the average ages of x members of a group is y year. A new member joins the group, then the new average of ages of members will be z year, then

Age of new Member is =

**[z - x(z - y)]**year8. If the average ages of x members of a group is y year and a member leaves the group, so the new average of ages of members will be z year, then the age of the member who leaves the group =

**[z + x ( y - z) ]**year9. If the average of n1 results is x1 and average of n2 results is x2, then the average of total (n1+n2) results will be

10. If a person covered a certain distance at a speed of x km/h and y Km/h respectively then the average speed of the person will be=

11. If a person covered a certain distance at a speed of x km/h, y km/h and z km/h respectively, then the average speed of the person will be=

## Questions Asked from this Chapter:

### Question Type 1: Based on Direct Formula Average = Sum of Quantities/Number of Quantities

**Example:**

The average weight of five persons sitting in a boat is 38 Kg. The average weight of the boat and the persons sitting in the boat is 52 Kg. What is the weight of the boat?

a) 228 Kg

b) 122 Kg

c) 232 Kg

d) 242 Kg

**Solution:**

### Question Type 2: If Average of "X" number is given, In which first "P" numbers & last "Q" numbers are given. Then Find the Nth Number.

**Example:**

### The average of nine numbers is 50. The average of first five numbers is 54 and that of the last three numbers is 52. Then the sixth number is:

a) 30

b) 34

c) 24

d) 44

**Solution:**

### Question Type 3: Based on Finding average of Consecutive Numbers

**Example:**

The average of first nine prime numbers is:

a) 9

b) 11

c) 11*(2/9)

d) 11*(1/9)

**Solution:**

**Example:**

The average of the first 100 positive integers is:

a) 100

b) 51

c) 50.5

d) 49.5

**Solution:**

**Example:**

The average of the odd numbers upto 100 is:

a) 50.5

b) 50

c) 49.5

d) 49

**Solution:**

**Example:**

The average of the sqaures of first 10 natural number is:

a) 35.5

b) 36

c) 37.5

d) 38.5

**Solution:**

**Example:**

The arithmetic mean(average) of the first 10 whole numbers is:

a) 5

b) 4

c) 5.5

d) 4.5

**Solution:**

### Question Type 4: If monthly incomes of "P & Q" , "Q & R", "P & R" are given. Then Find monthly incomes of P, Q, R

**Example:**

The average monthly salary of A and B is Rs 14000, that of B and C is Rs 15600, and that of A and C is Rs 14400. Monthly salary of B is:

a) Rs 12400

b) Rs 12800

c) Rs 15200

d) Rs 16000

**Solution:**

### Question Type 5: Based on Twice, Thrice, one third etc of Numbers

**Example:**

The average of three numbers is 28. The first number is half of the second, the third number is twice the second. Then the third number is:

a) 48

b) 36

c) 24

d) 18

**Solution:**

### Question Type 6: Average of a Collection of "X" measurements was calulated as "Y". But later a mistake was found, a number was wrongly recorderd as "A" instead of "B". Then Find Correct Average.

**Example:**

The average of 25 observations is 13. It was latter found that an observation 73 was wrongly entered as 48. The new average is:

a) 12.6

b) 14

c) 15

d) 13.8

**Solution:**

### Question Type 7: Based on making the runs/taking wickets in an inning by Cricketers

**Example:**

The bowling average of a cricketer was 12.4. He improves his bowling average by 0.2 points when he takes 5 wickets for 26 runs in the last match. The number of wickets taken by him before the last match was:

a) 125

b) 150

c) 175

d) 200

**Solution:**

**Example:**

A cricketer has a certain average of runs for his 8 innings. In the ninth innings, he scores 100 runs, thereby increases his average by 9 runs. His new average of runs is:

a) 20

b) 24

c) 28

d) 32

**Solution:**

### Question Type 8: Average of "X" numbers is "Y". If one number is excluded/ included/ increased/ replaced, then average becomes Z. Then Find excluded/ included/ increased/ replaced number.

**Example:**

The average weight of 12 parcels is 1.8 kg. Addition of another new parcel reduces the average weight by 50 grams. What is the weight of the new parcel?

a) 1.50 Kg

b) 1.10 Kg

c) 1.15 Kg

d) 1.01 Kg

**Solution:**

**Example:**

The average of 5 numbers is 27. If one number is excluded, the average becomes 25. The excluded number is:

a) 25

b) 27

c) 30

d) 35

**Solution:**