Q 1.

In C programming test the average marks of 120 students was 35. If the average of the passed students and failed students was 39 and 15 respectively. Find the numbers of students who passed and failed the test.

Pass 100, Fail 20

Pass 20, Fail 100

Pass 80, Fail 40

Pass 60, Fail 60

Total students N = 120

Average marks A = 35

Passed students average Ap = 39

Failed students average Af = 15

Let number of passed students be Np and number of failed students be (120 - Np).

Total marks scored by the class = NA = 120x35 = 4200

Total marks scored by passed students = NpAp = Np x 39

Total marks scored by failed students = (120 - Np)Af = (120 - Np) x 15

So, 4200 = (Np x 39) + [(120 - Np) x 15]

Or, 4200 = 39Np + 1800 - 15Np

Or, 24Np = 2400

Or, Np = 100

Number of passed students = 100

Number of failed students = 120 - Np = 20

Q 2.

The average weight of a class having 25 students is 38.4 kg. If the average weight of all the 15 boys of the class is 40 kg. Then find the average weight of the girls.

32

36

34

38

N = 25

A = 38.4

n = 15

a = 40

Total number of girls in the class = N - n = 25 - 15 = 10

Average weight of the girls = (NA - na)/10

= (25x38.4 - 15x40)/10

= 36

Q 3.

Average of 11 numbers is 36 and the average of the first 9 numbers is 34. If the last two numbers are in a ratio of 2:3 then find the smaller number.

32

34

36

40

N = 11

A = 36

n = 9

a = 34

Let the last two numbers be 2p and 3p.

Sum of the last two numbers = (NA - na)

= (11x36 - 9x34)

= 90

Sum of the last two numbers = 2p + 3p = 5p

Or, 5p = 90

Or, p = 18

Smaller number = 2p = 2x18 = 36

Q 4.

There are 30 girls in a piano class. If the average age of all the girls is 13 years and the average age of the first 18 girls is 15 years. Then find the average of the remaining 12 girls.

12

8

14

10

N = 30

A = 13

n = 18

a = 15

Average age of 12 girls = (NA - na)/12

= 10

Q 5.

The average of 4 consecutive even numbers is 27 then what is the greatest numbers?

26

28

30

32

Let the numbers be x, x+2, x+4, x+6

Sum = 4x + 12

Avg = (4x + 12)/4

Or, 27 = (4x + 12)/4

Or, x = 24

Therefore, greatest numbers = x+6 = 24+6 = 30

Q 6.

If the average of 8 numbers is 14 and the average of 6 of these numbers is 16. Then find the average of the remaining two numbers.

8

6

10

12

Given, N = 8

Average of 8 numbers A = 14

n = 6

Average of 6 numbers a = 16

Average of remaining two numbers is = (NA - na)/2

= (8x14 - 6x16)/2

= 8

Q 7.

Find the average of the squares of the first five whole numbers.

5

6

7

8

Sum of squares = 0+1+4+9+16 = 30

Avg = 30/5 = 6

Q 8.

Find the average of first 5 natural numbers.

1

2

3

4

Sum = 1+2+3+4+5 = 15

Avg = 15/5 = 3