Average

1. INTRODUCTION
Average
Generally, Average of two or more items can be defined as the result derived by
dividing the total-sum of items by the Numbers of items. However, the above
expression is only one type of Average. So, let us see types of Average.
Types of Average:-
(a) Mathematical Average:- it is further subdivided into three types.
1. Arithmetic Average
2. Geometric Mean
3. Harmonic Mean
(b)Averages of Position:- it is also further subdivided into two types.
1. Median
2. Mode
From our exam point of view, we will be studying Arithmetic Average only.
Important facts:-
(a) If a new person joins a group and the average age is increased then the age of new
person is more than the previous group average and vice-versa.
(b)If a person leaves a group and the average group is increased the average age of that
person is less than the average of the group and vice-versa.
(c) Average is calculated only if same category people or things or unit of calculated is
used.
Tricks Part I
Important Tricks
(a) If there is continuous numbers/continuous odd numbers/continuous even numbers
given then

The Average = (first number + last number)/2


Q1. What will be the average of 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46,
and 48?

Ans:- (22 + 48)/2 = 35

2. Q2. What will be the average of 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65 and 67?

Ans:- (43 + 67)/2 = 55

Have you noticed?
→ If there is n numbers in the question and n = odd number, then (n + 1)/2
th
number will be the average.
→ If there is n numbers in the question and n = even number, then (n/2
th
+ (n/2
+ 1)
th
)/2 will be the average.

(b) If the average of X numbers is M and N is added or subtracted or multiplied or
divided to all numbers, then

Average of new numbers = N will be added or subtracted or multiplied or
divided to M respectively.


Q3. The average of 12 numbers is 55 and if all the numbers are divided by 5 then
what will be the average of new numbers?

Ans:- Average of new numbers = 55/5 = 11.

Q4. The average of 15 numbers is 77 and if all the numbers are multiplied by 4 then
what will be the average of new numbers?

Ans:- Average of new numbers = 77 × 4 = 308.

(c) If Ajay travels at the speed of X km/h from home to playground and returns at the
speed of Y km/h. then what will be the average speed?

Ans:- Average speed = 2XY/(X + Y)
Q5. If Meera goes to her college at the speed of 5 Km/h and returns at the speed of
10 Km/h, then what is her average speed?

Ans:- Average speed = 100/15 = 6.7 Km/h (Approx

3. Tricks Part II
(a) In a group of X persons, average age is M yrs and if Y more persons join, average
age is increased by N yrs. Then calculate the age of new entrants to the group.

Ans:- Total age of newly joined persons = MY + (X+Y)N yrs
Q6. In a group of 20 employees, the average salary is Rs. 15,000/month and if 10
more persons join, the average salary is increased by Rs.5000/month. Then calculate
the average salary of newly joined employees.
Ans:- Total salary of newly joined employees = 5,000 × 30 + 15,000 × 10 = 3,00,000
Rs.
So, average salary = Rs.30,000/month
(b)In a group of X persons, average age is M yrs and if Y more persons join, average
age becomes N yrs. Then calculate the age of new entrants to the group.

Ans:- Total age of newly joined persons = MY + (X+Y)(N-M)

Note:- If in the above question, Y persons leave the group instead of new persons
joining it, the expression will be like this:-
Total age of persons left the group = MY + (X-Y)(N-M)
Q7. In a group of 20 employees, the average salary is Rs. 15,000/month and if 10
more persons join, the average salary becomes Rs.5000/month. Then calculate the
average salary of newly joined employees.
Ans:- Total salary of newly joined employees = 5,000 × 30 + (5,000 – 10,000) × 10
= 50,000 Rs. So, average salary = Rs.5,000/month ( ooooouch!so less salary only
due to some change of words in question)
(c) If the average of X results is Y and the average of first A results is M and average
of last A results is N. then calculate the A
th
and (A+1)
th
result.

Ans:- A
th
result = (AM+AN) – XY

(A+1)
th
result = XY – (AM+AN)

Q8. The average age of 08 students of 10
th
class is 15 yrs. If the average of first four
students is 18 yrs and last four students 16 yrs, then what is the age of fourth student?

Ans:- Age of fourth student = (4 × 18 + 4 × 16) – 8 × 15 = 16 yrs

Q9. The average age of 09 students of 8
th
class is 12 yrs. If the average of first four
students is 12 yrs and last four students is 10 yrs, then what is the age of fifth student?

4. Ans:- Age of fifth student = (12 × 9) – (48 + 40) = 20 yrs (That student would be
like me – mandbudhi)


Tricks Part II

(a) In a group of X persons, average age is M yrs and if Y more persons join, average
age is increased by N yrs. Then calculate the age of new entrants to the group.

Ans:- Total age of newly joined persons = MY + (X+Y)N yrs
Q6. In a group of 20 employees, the average salary is Rs. 15,000/month and if 10
more persons join, the average salary is increased by Rs.5000/month. Then calculate
the average salary of newly joined employees.
Ans:- Total salary of newly joined employees = 5,000 × 30 + 15,000 × 10 = 3,00,000
Rs.
So, average salary = Rs.30,000/month
(b)In a group of X persons, average age is M yrs and if Y more persons join, average
age becomes N yrs. Then calculate the age of new entrants to the group.

Ans:- Total age of newly joined persons = MY + (X+Y)(N-M)

Note:- If in the above question, Y persons leave the group instead of new persons
joining it, the expression will be like this:-
Total age of persons left the group = MY + (X-Y)(N-M)
Q7. In a group of 20 employees, the average salary is Rs. 15,000/month and if 10
more persons join, the average salary becomes Rs.5000/month. Then calculate the
average salary of newly joined employees.
Ans:- Total salary of newly joined employees = 5,000 × 30 + (5,000 – 10,000) × 10
= 50,000 Rs.
So, average salary = Rs.5,000/month ( ooooouch!so less salary only due to some
change of words in question)
(c) If the average of X results is Y and the average of first A results is M and average
of last A results is N. then calculate the A
th
and (A+1)
th
result.

Ans:- A
th
result = (AM+AN) – XY

(A+1)
th
result = XY – (AM+AN)

5. Q8. The average age of 08 students of 10
th
class is 15 yrs. If the average of first four
students is 18 yrs and last four students 16 yrs, then what is the age of fourth student?

Ans:- Age of fourth student = (4 × 18 + 4 × 16) – 8 × 15 = 16 yrs

Q9. The average age of 09 students of 8
th
class is 12 yrs. If the average of first four
students is 12 yrs and last four students is 10 yrs, then what is the age of fifth student?

Ans:- Age of fifth student = (12 × 9) – (48 + 40) = 20 yrs (That student would be
like me – mandbudhi)