The most famous topic among the most important topics of mathematics is the average formula, because under this, special questions based on practical knowledge like average run, average age, average score, average weight, average speed etc. are asked in the competitive examination.
It is necessary to understand the basic units of Average Formula and its basic units to provide complete knowledge to the students i.e. competitor. Keeping in mind the competitive examination, here such formulas and tricks have been included which are most used in solving the questions of average.
In simple words, the quotient obtained by dividing the sum of two or more similar quantities by the same number of quantities is called the average of those quantities.
 |
| (IQ Curator - Average Tricks for All Competitive Exams | औसत का फार्मूला, ट्रिक और परिभाषा) |
Basic Formula of Average = Sum of Data / Number of Data
Or
Total amount = Average x Number of data
Let us now see the questions which are often asked in competitive examinations from this section.
1st type questions can also come in the exam.
Such questions are very simple, in which questions related to only and only numbers come, like – average of some numbers can be given, or the average will be given and the sum of the numbers will be asked, let's see now like this Some questions-
1. What will be the average of the numbers from 1 to 19-
Its simple formula is- = n + 1
2
= 19 + 1 = 10 Answer
2
2. Find the average of the first 5 even numbers
Formula= (n+1) = 5+1= 6
i., but if given that find the average of odd numbers
Then the answer would be = n = 5 Answer
3. There is a type of question in which there is an equal difference in numbers called series of consecutive numbers, their average is asked
For example, take the average of 5, 8, 11, 14, 17………47,
There is a very simple formula to calculate its average, remember it
= first number + last number
2
= 47 + 5
2
= 26 Answers
4. Similarly, the questions that are asked here, the formulas of all are being provided, after that we will see other types of questions.
a. Average of even numbers from 1 to n
= last even number + 2
2
* If the last number is even,
but if odd
so = last number + 1
2
In another way you can do if last even number is given then immediately preceding even number is considered as last even number, e.g., if last number is given 45 then last even number will be 44, and average will be 23,
b. Average of odd numbers from 1 to n
In such type of questions, we just have to find that how many odd numbers are there from 1 to n and as you know that the average of odd numbers is their number in such case
For example, find the average of the odd numbers from 1 to 9 - or - find the average of the numbers from 1 to 10
In the first case we have to divide (9+1) by 2 and the answer will come and in the second case we just have to divide 10 by 2 because half the numbers are even and half odd
c. Average of squares of natural numbers-
= (n+1) (2n+1)
6
(where "n" is the last number)
d. Average of cubes of first natural numbers = n(n+1)2
4
(where "n" is the last number)
2nd type questions can also come in the exam.
1. The average age of 30 students of a class is 14 years, if the age of a teacher is also included, then the average age becomes 15 years. Find the age of the teacher.
There is a simple formula for this and you can also take it verbally without formula, they will know later first formula
= new average + old number of members x average increase
= 15 + 30 x 1
= 45 Answer
2. The average weight of four persons increases by 3 kg if another person is included in place of the one who weighs 120 kg.
This question can also be done from the previous formula
= 120 + 4 x 3
= 132 kilograms Answer
3. If a person covers a certain distance at the speed of X km/h and the same distance at the speed of Y km/h, what will be his average speed?
Its simplest formula is
= 2xy
x+y and if he moves with three different speeds (xyz)
so, the formula would be
= 3 xyz
xy+yz+zx
4. The average age of three boys is 15 years. If their ages are in the ratio 3:5:7, what will be the age of the youngest boy?
Solution:
Total age of all the three boys will be = 15 x 3 = 45 years
Now divide 45 years in the ratio 3: 5: 7 Your answer will come
= 45
3+5+7
= 45
15
= 3
Now since the age of the youngest boy is asked, we will multiply it by the ratio of the youngest boy
= 3 x 3 = 9 years Answer
5. The average of the marks obtained by 40 students of a class is 86 if the highest 5 marks are excluded then the average decreases by one mark Find the average marks of the top 5 students?
Solution:
First of all, we will just find the sum of the digits
= 86 x 40 = 3440
Now the sum that will be formed after taking out those five digits is
= 35 x 85 = 2975
Difference of both = 3440 – 2975 = 465
This is the sum of those five digits, now we will calculate its average
= 465
5
= 93 Answer
6. The average age of four sisters is 7 years. If the mother's age is included, the average age increases by 6 years, then the mother's age will be?
Solution:
Firstly, total age of 4 sisters = 7 x 4 = 28
Now when the mother's age is included, the average becomes = 13
And total people = 4 sister + mother = 5
So total age = 13 x 5 = 65
So, mother's age = 65- 28 = 37 years
From Average Short Trick –
= new average + old number of members x average increase
= 13 + 4 x 6
= 37 years Answer
7. A cricket player had some average of 10 innings he scored 108 runs in the 11th innings and this increased his average run count by 6 Now what is his average run count?
Solution-
n innings = 11
Runs scored = 108
Average increase = 6
Required average run count = n runs scored in the last innings -(n-1) x increase in average
=108 – (11-1) x 6
=108-60
= 48 runs Answer
8. The average run count of 6 players in a cricket match was 36. If one of these players scored 16 runs, then what is the average run count of the remaining players?
Solution:
Total runs = 36 x 6 = 216
One of these players has scored 16 runs, deduct them
= 216- 16
= 200
Hence the average of the remaining players
= 200/5 = 40 Answer
3rd type questions can also come in the exam.
1. The average age of 30 students of a class is 14 years, if the age of a teacher is also included, then the average age becomes 15 years. Find the age of the teacher?
There is a simple formula for this and you can also take it verbally without formula, they will know later first formula
= new average + old number of members x average increase
= 15 + 30 x 1
= 45 Answer
2. The average weight of four persons increases by 3 kg if another person is included in place of the one who weighs 120 kg?
This question can also be done from the previous formula
= 120 + 4 x 3
= 132 kilograms Answer
3. If a person covers a certain distance at the speed of X km/h and the same distance at the speed of Y km/h, what will be his average speed?
Its simplest formula is
= 2xy
x+y and if he moves with three different speeds(xyz)
so, the formula would be
= 3 xyz
xy+yz+zx
4. The average age of three boys is 15 years. If their ages are in the ratio 3:5:7, what will be the age of the youngest boy?
Solution:
Total age of all the three boys will be = 15 x 3 = 45 years
Now divide 45 years in the ratio 3: 5: 7 Your answer will come
= 45
3+5+7
= 45
15
= 3
Now since the age of the youngest boy is asked, we will multiply it by the ratio of the youngest boy
= 3 x 3 = 9 years Answer
5. The average of the marks obtained by 40 students of a class is 86 if the highest 5 marks are excluded then the average decreases by one mark Find the average marks of the top 5 students?
Solution:
First of all, we will just find the sum of the digits
= 86 x 40 = 3440
Now the sum that will be formed after taking out those five digits is
= 35 x 85 = 2975
Difference of both = 3440 – 2975 = 465
This is the sum of those five digits, now we will calculate its average
= 465
5
= 93 Answer
6. The average age of four sisters is 7 years. If the mother's age is included, the average age increases by 6 years, then the mother's age will be?
Solution:
Firstly, total age of 4 sisters = 7 x 4 = 28
Now when the mother's age is included, the average becomes = 13
And total people = 4 sister + mother = 5
So total age = 13 x 5 = 65
So, mother's age = 65- 28 = 37 years
From Short Trick –
= new average + old number of members x average increase
= 13 + 4 x 6
= 37 years Answer
7. A cricket player had some average of 10 innings he scored 108 runs in the 11th innings and this increased his average run count by 6 Now what is his average run count?
Solution-
n innings = 11
Runs scored = 108
Average increase = 6
Required average run count = n runs scored in the last innings -(n-1) x increase in average
=108 – (11-1) x 6
=108-60
= 48 runs Answer
8. The average run count of 6 players in a cricket match was 36. If one of these players scored 16 runs, then what is the average run count of the remaining players?
Solution:
Total runs = 36 x 6 = 216
One of these players has scored 16 runs, deduct them
= 216- 16
= 200
Hence the average of the remaining players
= 200/5 = 40 Answer
Good Luck!
lse" Priority="62" Name="Light Grid"/>
