Average Problems Shortcut Tricks
Average Methods
Average Shortcut Tricks are very important things in competitive exam. Time takes a huge part in competitive exams. If you know time management then everything will be easier for you. Most of us miss that part. Few examples on average shortcuts is given in this page below. We try to provide all types of shortcut tricks on average here. We request all visitors to read all examples carefully. These examples here will help you to better understand shortcut tricks on average.
Before doing anything we recommend you to do a math practice set. Then find out twenty math problems related to this topic and write those on a paper. Solve first ten math problems according to basic math formula. You also need to keep track of Timing. After solving all ten math questions write down total time taken by you to solve those questions. Now practice our shortcut tricks on average and read examples carefully. After doing this go back to the remaining ten questions and solve those using shortcut methods. Again keep track of the time. This time you will surely see improvement in your timing. But this is not all you need. If you need to improve your timing more then you need to practice more.
You all know that math portion is very much important in competitive exams. That doesn’t mean that other sections are not so important. You can get a good score only if you get a good score in math section. Only practice and practice can give you a good score. All you need to do is to do math problems correctly within time, and only shortcut tricks can give you that success. But it doesn’t mean that without using shortcut tricks you can’t do any math problems. You may have that potential to do maths within time without using any shortcut tricks. But other peoples may not do the same. So Average shortcut tricks here for those people. We try our level best to put together all types of shortcut methods here. But it possible we miss any. We appreciate if you share that with us. Your little help will help so many needy.
What is Average?
The result obtained by adding several quantities together and then dividing this total by the number of quantities is called Average . The main term of average is equal distribution of a value among all which may distribute persons or things . We obtain the average of a number using formula that is sum of observations divide by Number of observations .
Here is average based some fact and formula and some average shortcut tricks examples . The problem are given in Quantitative Aptitude which is a very essential paper in banking exam . Under below given some more example for your better practice.
Anything we learn in our school days was basics and that is well enough for passing our school exams . Now the time has come to learn for our competitive exams . For this we need our basics but also we have to learn something new . That’s where shortcut tricks are comes into action.
Average Formula:
Average: = ( Sum of observations / Number of observations ).
Find the Average Speed
Suppose Rahul covers a certain distance at P Kmph and an equal distance at O Kmph. Then,
the average speed during the whole journey is (2PO / P + O ) Kmph.
Find the Average of all numbers ?
There are Five Numbers,we are going to calculate the average of 29, 31, 33, 37, 49.
Average = (29 + 31 + 33 + 37 + 49 ) / 5 = 179 / 5 = 35.8.
Example 1:
The average of five numbers is 29. if one number is exclude the average becomes 27. what is the exclude number ?
Answer :
let the exclude number is
= ( 29 x 5 ) – ( 27 x 4 )
= 145 – 108
= 37 .
Example 2:
Find the average of first 20 natural numbers ?
Answer :
Sum of first n natural numbers = n ( n + 1 ) /2
So, we can find easily average of first 20 natural numbers 20 x 21 / 2 = 210
So, then Required average is = 210 / 20 = 10.5.
Example 3:
Find the average of first 20 multiplies of 5 .
Answer:
Required average = 5 ( 1 + 2 + 3 +……………….. + 20) /20
= ( 5 x 20 x 21 / 20 x 2) = 2100 / 40 = 52.5 .
So the Required average is 52.5.
Example 4 :
The average of 13 result is 40 , that of the first six is 30 and that of the last six is 32 . Find the value of the 7th number .
Answer :
Shortcut tricks :
7th number = Total of 13 result – ( Total of first six + Total of last six results )
= 13 x 40 – ( 6 x 30 + 6 x 32 )
= 520 – 180 + 192
= 148 .
Average Methods Example 1
In this average methods Example 1 we discuss some examples which help your better understanding in average chapter which came in most competitive exams.This is the basic theory of average which applied in question to obtain answers here is Average Methods of example 1 in different form of examples.
This type of problem are given in Quantitative Aptitude which is a very essential paper in banking exam.Under below given some more example for your better practice.
Example 1:
There are two section X and Y of a College, consisting of 36 and 44 studentsrespectively.if the average weight of section X is 40Kg and that of section Y is 35Kg . Find the average weight of the whole College (in Kg)?
Answer:
Step 1: At first the total ( X + Y ) college students are ( 36 + 44 ) = 80.
Step 2: college X total student weight and college Y total student weight is ( 36 x 40 + 44 x 35 ) = 2980
Average weight of the whole college is = 2980 / 80 = 37.25.
Example 2:
In a School 8 student average weight is increased by 3.5 kg when new student comes in place of one of them than weight become 55 kg what might be the weight of the new student?
Answer :
Step 1: At first we find the total weight increased So, ( 8 X 3.5 )kg = 28kg.
Step 2: Now the weight of new Student is = ( 55 + 28 )kg = 83 kg.
So, the weight of the new student is 83 kg.
Example 3:
The Average weight 3 girls A, B, and C is 55kg,While the average weight of three boys B, D, and E is 57 kg. What is the average weight of A, B, C, D, E ?
Answer :
Step 1: At First we find 3 girls total weight ( A + B + C ) = ( 55 X 3 ) = 165 kg. and Total 3 boys weight of ( B + D + E ) = ( 57 x 3 ) = 171.
Step 2: Adding both weight of ( A + 2B + C + D + E ) = ( 165 + 171 ) = 336 kg.
Note: So, to find the average weight of A B C D and E, we duty to know B’s weight, which is not given. So the data is inadequate.
Example 4: Divya obtain 56, 75, 78, 86 and 88 marks out of 100 in Physics, Life Science, Mathematics, Biology, and Computer. What are her average marks ?
Answer :
Step 1: Average of all subject marks 56 + 75 + 78 + 86 + 88 / 5
=383 / 5 = 76.6.
Example 5: Find the average of all the numbers between 6 and 34 which are divisible by 5.
Answer:
Step 1: 10 + 15 + 20 + 25 + 30 which are divisible by 5 in between 6 and 34
So average of number is 10 + 15 + 20 + 25 + 30 / 5 = 100 / 5 = 20.
Average Methods Example 2
The result obtained by adding several quantities together and then dividing this total by the number of quantities is called Average.This is the basic theory of Speed Time and Distance which is applied in question to obtain answers here is Speed Time and Distance Methods of example 2 in different form of examples.
In maths exam papers there are two or three question are given from this chapter.This type of problem are given in Quantitative Aptitude which is a very essential paper in banking exam.Under below given some more example for your better practice.
Example 1:
The average age of 34 students in a school is 15 years, after that when geography teacher’s age is added to student age then the average age increases by one, Find what is the teacher’s age in years?
Answer :
Step 1:T first we find the total student ages with out adding teacher’s age that is ( 34 x 15 ) = 510 years.
Now we find out the age of students adding with teachers age that is ( 35 x 16 ) = 560 years.
Step 2: Teachers age is ( 560 – 510 ) = 50 years.
Example 2:
The average age of 45 students in a batch is 18 years. The average age of 23 students is 16 years. Find average age of remaining 16 students ?
Answer :
Step 1: At first we find the age total age of 45 and 23students is (45 x 18 ) = 810 and ( 23 x 16 ) = 368.
Step 2: Sum of the ages of 16 students is = ( 810 – 368 ) = 442.
So average age of is ( 442 / 16 ) = 28 years.
Example 3:
The weight of 5 tanks of 57Kgs, 42Kgs, 45Kgs, 63Kgs,74Kgs.Find its average?
Answer:
Average = 58 + 42 + 45 + 63 + 74 / 5
= 282 / 5 = 56.4.
Example 4: What is the average of the first 6 prime numbers ?
Answer : 2 + 3 +5 + 7 + 11 + 13 / 6
= 41 / 6 = 6.83.
Example 5: The average of a non-zero number and its square is 5 times the number. The number is.
Answer : Let the number be x . Then,
x + x^2 / 2 = 5x
x^2 -9x = 0
x( x – 9 ) = 0 or x = 0 or x = 9
So the number is 9.
Average Methods Example-3
In average chapter we can say more properly and Enumeration mean is rectified terms, we can say that average is an sum of n number and divided by n.
we elaborate this a student score in 35, 56, 65 in three different subjects respectively, than the average score in subject is 35 + 56 + 65 / 3 = 52. So here is some average methods and shortcut tricks example 3 we discuss. This type of problem are given in Quantitative Aptitude which is a very essential paper in banking exam. Under below given some more example for your better practice.
Example 1:
The average marks acquired by 140 students in a final examination is 36.If the average marks of failed students is 18 and the passed average students is 30. What is thepassed students in examination.
Answer :
Number of passed students are = Total students(total average – failed average) / passed average – failed average
Step 1: = 140 ( 36 – 18 ) / ( 30 – 18 )
Step 2: = 210
Example 2:
The average marks of 3 group of 54, 62 and 48 respectively is 60, 65, 70,Then Find the average marks of all the students ?
Answer :
Step 1: At First we find the total students marks according with 3 group = (54 x 60 + 62 x 65 + 48 x 70) = ( 3240 + 4030 + 3360 ) = 10630.
Step 2: Now we need to find average marks (54 + 62 + 48 ) = 164, Required average = 10630 / 164 = 64.81.
Example 3:
Sabir obtained 75,55,89,65 and 45 marks (out of 100) in Economy , Bengali, History, Geography, Environmental science, .What are his average marks.
Answer :
First we add all the obtain number than divide by number of subject,
Average : 75 + 55 + 89 + 65 + 45 / 5 = 65.8
Example 4: The average of six numbers is x and average of three of these is y. if the average of the remaining three is z ,
Answer : Here we have x is average of three of these is y so , 3y and average of the remaining three is z so, 3s
average of six numbers is
x = 3y + 3z / 6 = 3 ( y + z ) / 6
x = ( y + z ) / 2
2x = y + z .
Example 5: A city center has an average of 610 visitors on Sunday and 340 on other days. The average number of visitors per day in a month of 30 days Beginning with a Sunday is.
Answer : Since the month begins with a Sunday, So there will be five Sundays in the month
= ( 610 x 5 + 340 x 25 )/ 30
= 3050 + 8500 / 30
=11550 / 30 = 385.
Average Methods Example 4
The result obtained by adding several quantities together and then dividing this total by the number of quantities is called Average. This is the basic theory of average which applied in questions to obtain answers here is Average Methods of example 4 and shortcut tricks in different form of examples.
This type of problem are given in Quantitative Aptitude which is a very essential paper in banking exam. Under below given some more example for your better practice.
Example 1:
The average of Six numbers is 25 and if one number of that average is cropped than the average occur is 26. Find the cropped number?
Answer :
here We can find the cropped number that is
Step 1:average of six number with cropped number is = (25 X 6) = 150 and average five number without cropped number is = (26 X 5) = 130.
Step 2: now the cropped number is = ( 150 – 130 ) = 20.
Here the cropped number is 20.
Example 2: The average of 40 numbers is 20. If two numbers 36 and 30 are discarded then Find the average of the remaining numbers ?
Answer :
Step 1 : At First we find the total number so ( 40 x 20 ) = 800. So sum 40 number is 800.two number discarded, so remaining 48 numbers is = ( 800 -( 36 + 30 ) = 734.
Step 2: Here we find required average is = 734 / 38 = 19.31.
Example 3:
If average of two numbers is 77.5 and a number is 5.5 less than the average, then what is the second number?
Answer:
77.5 x 2 = 155
77.5 – 5.5 = 72
second number is ( 155 – 72 ) = 83
Example 4:
Find the average of the following set of scores ?
357 , 854 , 214 , 648 , 478
Answer :
2551 / 5
= 510.2
So the average of five numbers is 510.2.
Example 5:
What is the average of the following set of scores ?
252 , 333 , 622 , 525 , 445 , 710 , 875
Answer :
3762 / 7
= 537.42
So the average of five numbers is 537.42
Average Methods Example 5 :
The result obtained by adding several quantities together and then dividing this total by the number of quantities is called Average.This is the basic theory of average which applied in question to obtain answers here is Average Methods of example 5 and shortcut tricks in different form of examples.
This type of problem are given in Quantitative Aptitude which is a very essential paper in banking exam.Under below given some more example for your better practice.
Example 1:
The average run of a cricket player of 8 innings was 34. How many runs must he make in his next innings so as to increase his average of runs by 6 ?
Answer :
Step 1: Average run of a player in next innings is 9 = ( 34 + 6 ) = 40 runs.
Step 2: Required run for 9 innings is ( 40 x 9 ) = 360 runs and 8 innings is ( 34 x 8 ) = 272 runs.
So, Required number of run is = (360 – 272 ) = 88 runs.
Example 2:
The average age of 15 boys is 18 years in the Maths class and that of 13 girls is ages 15 years.What is the average age of total maths class ?
Answer :
In a maths class 15 boys ages 18 years = ( 15 x 18 ) = 270
In a maths class 13 girls ages 15 years = ( 13 x 15 ) = 195
So average age of total maths class is = 270 + 195 / 28 = 465 / 28 = 16.607
Example 3:
The average of five consecutive odd numbers A, B, C, D, and E is 45.what is the product of A and D ?
Answer :
A B C D E
43 45 47 49 51
So the Product of A and D is = ( 43 x 49 ) = 2107.
Example 4: In a shop out of 9 persons , 8 persons spent Rs. 30 each for their shopping. The ninth one person spent Rs. 20 more than the average expenditure of all the nine. The total money spent by all of them.
Answer:
Let the average money spent be Rs. x, Then
9x = 8 x 30 + (x + 20 )
9x = x + 260
8x = 260
x =32.50.
Total money spent by = 9x = 9 x 32.50 = 292.50.
Example 5: Four years ago, the average age of Rajesh and Suresh was 16 years. With Dipika joining them, the average age becomes 24 years. How old Dipika now ?
Answer :
Present age of ( Ramesh + Suresh ) = ( 16 x 2 + 4 x 2 ) = 40 years.
Present age of ( Ramesh + Suresh + Dipika ) = ( 24 x 3 ) = 72.
Dipika present age is ( 72 – 40 ) = 32.
Average Methods Example 6 :
The result obtained by adding several quantities together and then dividing this total by the number of quantities is called Average.This is the basic theory of average which applied in question to obtain answers here is Average Methods of example 5 and shortcut tricks in different form of examples.
This type of problem are given in Quantitative Aptitude which is a very essential paper in banking exam.Under below given some more example for your better practice.
Example 1:
The average monthly income of A and B is Rs.6040. The monthly average income of B and C is Rs.7500 and monthly average income of A and C is Rs. 6500. Find the income of A in a monthly income ?
Answer:
Step 1: here is ABC given respectively monthly income, hence we need to find both income.
( A + B ) = ( 6040 x 2 ) = 12080, ( B + C ) =( 7500 x 2 ) = 15000, ( C + A ) = ( 6500 x 2 ) = 13000
Step 2: If we add 3 income 2( A + B + C ) = 2 x ( 12080 + 15000 + 13000 ) = 40080 or A + B + C = 40080 / 2 = 20040.
Step 3: So we get the income of A Subtract income of ( A + B + C ) – ( B + C ) = (20040 – 15000 ) = 5040.5
Example 2:
The average of Five numbers is 62.The average of the second and the third number is 45.The average of the first and the fifth number is 66. What is the fourth number ?
Answer :
Average of Five numbers is = 62 x 5 = 310
Average of second and third number = 45 x 2 = 90
Average of first and fourth number = 66 x 2 = 132
( 132 + 90 ) = 222
The fourth number is ( 310 – 222 ) = 88
Example 3:
The average of 5 numbers is 4.5.If average of two number is 3.5 and that of another two numbers is 3.7,then what is the last number?
Answer :
2 x 3.5 = 7
2 x 3.7 = 7.4
5 x 4.5 = 22.5
( 22.5 – 7.4 + 7 ) = 8.1
So the last number is 8.1.
Example 4:
The average of 4 consecutive odd numbers P , Q , R , S is 66.What is the product of P and S?
Answer :
Average is 66
P Q R S
63 64 65 66 67 68 69
Product of ( P x S ) = ( 63 x 69 ) = 4347.
Example 5:
In a school of class x after replacing an old student by new student, it was found that the average age of eight student of a class x is the same as it was 5 years ago. What is the differences between the ages of the replaced and new student ?
Answer : Age decreased = ( 8 x 5 ) = 40 years.
So the required age difference is = 40 years.
Tag :
Average
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