Average - Arithmetic

Question (1) The average age of 30 students is 7. The average age becomes 8 when the age of a teacher is added. Find the age of teacher.

Solution :

Given, average age of 30 students = 7

Average age of 30 students and 1 teacher = 8

Therefore, age of teacher = ?

Now, the total age of 30 students = 30 × 7 = 210

And total age of 30 students + 1 teacher (31 person) = 31 × 8 = 248

Thus, age of teacher = (total age of 30 students + 1 teacher ) – (Total age of 30 students)

= 248 – 210 = 38

Thus, Age of teacher = 38 years Answer

Question (2) Average weight of 20 students is equal to 32 kg. If average weight becomes 33 after adding the weight of one of their teacher, then what will be the weight of teacher?

Solution :

Given, average weight of 20 students = 32 kg

And average weight of 20 students and 1 teacher = 33 kg

Then weight of teacher = ?

Total weight of 20 students = 32 kg × 20 = 640 kg

And total weight of 20 students and 1 teacher, i.e. 21 persons = 33 kg × 21 = 693

Thus, weight of teacher = weight of 20 students and 1 teacher – weight of 20 students

= 693 – 640 = 53 kg

Thus, weight of teacher = 53 kg Answer

Question (3) Average age of 25 students is 9 years. When the age of a teacher is added to the age of students, the average increases by 2; what will be the age of teacher?

Solution :

Given, Average age of 25 students = 9 years

And average increases by 2, i.e. = 11 when age of teacher is added

Thus, age of teacher = ?

The total age of students = number of students × average age

= 25 × 9 = 225

The total age of students + teacher = (numbers of students + number of teacher) × average age

= (25 + 1) × 11

= 26 × 11 = 286

Thus, age of teacher = age of students along with teacher – age of students

= 286 – 225 = 61 years

Thus, age of teacher = 61 years Answer

Question (4) The average weight of football players is 50 kg and the average weight of hockey player is 60 kg. If there are 20 football players and 30 hockey players, what will be the average weight of total players?

Solution:

Given, number of football players = 20

Average weight of football players = 50 kg

Number of hockey players = 30

Average weight of hockey player = 60 kg

Therefore, average weight of total players = ?

The total weight of football players = Number of players × Average weight

= 20 × 50 kg = 1000 kg

The total weight of hockey players = Number of players × Average weight

= 30 × 60 kg = 1800 kg

Now, total number of players = number of football players + number of hockey players

= 20 + 30 = 50

And total weight = total weight of football players + total weight of hockey players

= 1000 kg + 1800 kg

= 2800 kg

Now, we know that, average

Thus, average weight of total players

= 56 kg

Thus, average weight of total players = 56 kg Answer

Question (5) There are 20 girls and 30 boys in a class. If the average weight of girls is 35 kg and average weight of boys is 40 kg, what is the average weight of total students?

Solution :

Given, number of girls = 20

Average weight of girls = 35 kg

Number of boys = 30

Average weight of boys = 40 kg

Thus, average weight of total students = ?

Total weight of girls = Number of girls × Average weight

= 20 × 35 kg

⇒ Total weight of girls in class = 700 kg

Total weight of boys = Number of boys × Average weight

= 30 × 40 kg

⇒ Total weight of boys in class = 1200 kg

Now total weight of all students = total weight of girls + total weight of boys

= 700 kg + 1200 kg = 1900 kg

Thus, total weight of all the students = 1900 kg

And total number of students = no. of girls + number of boys

= 20 + 30 = 50

Thus, average weight of total students = total weight / total number of students

= 38 kg

Thus, average weight of total students = 38 kg Answer

Question (6) The average age of students in class 3 is 9 years. And the average age of students in class 5 is 10 years. If the number of students in class 3 is 40 and number of students in class 5 is 50, then find the average age of all of the students.

Solution:

Given, total number of students in class 3 = 40

Average age of students in class 3 = 9 years

Total number of students in class 5 = 50

Average age of students in class 5 = 10 years

Thus, average age of all of the students = ?

Now,

Total age of students = number of students × average age

Thus, total age of students in class 3 = 40 × 9 years

= 360 years

And total age of students in class 5 = 50 × 10 years

= 500 years

Now. Total age of students = total age of students in class 3 + total age of students in class 5

= 360 years + 500 years

= 860 years

Total number of students = number of students in class 3 + number of students in class 5

= 40 + 50 = 90

Average age of total students = total age of students / number of total students

=860/90 years = 9.55 years

Thus, average age of total students = 9.55 years Answer

Question (7) Out of 100 Ryan got 40 marks in English, 70 marks in mathematics, 60 marks in Physics and 50 marks in Chemistry. What are the average marks or Ryan?

Solution :

Given, marks in English = 40

Marks in Mathematics = 70

Marks in Physics = 60

Marks in Chemistry = 50

Total number of subject = 4

Thus, average marks of Ryan = ?

We know that, Average

Thus, average marks = Total marks in all subject/number of subject

=220/4 = 55

Thus Average marks of Ryan = 55 Answer

Question (8) The average of 3, 2, p, and 6 is equal to 4, and the average of 3, 4, 6, and p and q is equal to 6. Then find values of p and q.

Solution:

Given, average of 3, 2, p and 6 = 4

And, average of 3, 4, 6, p and q = 6

Then, p and q = ?

Now, we know that, average

Thus, average of 3, 2, p and 6

⇒ 4 = (11+p)/4`" inline="" layout="container">

After cross multiplication we get,

4 × 4 = 11 + p

⇒ 16 = 11 + p

⇒ 11 + p = 16

⇒ p = 16 – 11

⇒ p = 5

And, average of 3, 4, 6, p and q

⇒ 6

After cross multiplication, we get

6 × 5 = 13 + p + q

⇒ 30 = 13 + p + q

⇒ 13 + p + q = 30

After substituting the value of p = 5, we get

13 + 5 + q = 30

⇒ 18 + q = 30

⇒ q = 30 – 18

⇒ q = 12

Thus, p = 5 and q = 12 Answer

Question (9) The average of 9, 13 and p is equal to 11. If the average of 8, p, 15, q and 21 is equal to 15, then find the value of p and q

Solution :

Given, Average of 9, 13 and p = 11

And, average of 8, p, 15, q and 21 = 15

Thus, value of p and q = ?

We know that, Average

Thus, average of 9, 13 and p

⇒ 11

After cross multiplication, we get

11 × 3 = 22 + p

⇒ 33 = 22 + p

⇒ 22 + p = 33

⇒ p = 33 – 22

⇒ p = 11

Again, the average of 8, p, 15, q and 21

⇒ 15

After cross multiplication, we get

15 × 5 = 44 + p + q

⇒ 75 = 44 + p + q

⇒ 75 – 44 = p + q

⇒ 31 = p + q

⇒ p + q = 31

After substituting the value of p we get,

11 + q = 31

⇒ q = 31 – 11

⇒ q = 20

Thus, p = 11 and q = 20 Answer.

Question (10) The average of three consecutive odd numbers is 13. When a fourth odd number is added to it the average is increased by 3, then find the fourth number.

Solution:

Given, average of three consecutive number = 13

And average of three consecutive odd number + one number = 13 + 3

Therefore, 4^th number = ?

Let first odd number = m

Therefore, second odd number = m + 2

And, third odd number = m + 4

Now, we know that, average

Thus, average of three consecutive odd numbers = sum of numbers / 3

⇒ 13

⇒ 13

After cross multiplication, we get

13 × 3 = 3 m + 6

⇒ 39 = 3 m + 6

⇒ 3 m + 6 = 39

⇒ 3 m = 39 – 6

⇒ 3 m = 33

⇒ 3 m = 11

Therefore, second number = m + 2

= 11 + 2 = 13

And, third number = m + 4

= 11 + 4 = 15

Thus, odd numbers are 11, 13 and 15

Now, let a number q is added to the numbers

Then average + 3 = sum of numbers / 4

⇒ 13 + 3

⇒ 16 `=(39+q)/4`" inline="" layout="container">

After cross multiplication, we get

16 × 4 = 39 + q

⇒ 64 = 39 + q

⇒ 64 – 39 = q

⇒ 25 = q

⇒ q = 25

Thus, fourth odd number which was added = 25 Answer