Brief Summary
This YouTube video by Maths Mania provides a comprehensive explanation of averages, focusing on the concept of alligation and its applications in various problem-solving scenarios. The video covers basic average calculations, alligation techniques, and problem-solving strategies with real-world examples.
- Introduces the concept of average and alligation.
- Explains how to apply alligation in different scenarios.
- Provides examples and step-by-step solutions to various average-related problems.
Introduction to Averages and Alligation
The video begins by explaining the basic concept of average as the sum of values divided by the number of values. It illustrates this with an example of calculating the average salary of 20 people, emphasizing that the average represents an equal distribution of the total sum. The concept of alligation is introduced as a method to solve problems where the average of a total part is known, along with the averages of its individual parts.
Understanding Alligation with Class 10th Example
The video uses the example of class 10th students divided into sections A and B to illustrate alligation. The average age of all students is given as 17, with section A averaging 19 and section B averaging 16. The problem involves finding the ratio of students in sections A and B. The solution involves understanding that the average value lies between the individual values and using subtraction to find the ratio.
Applying Alligation to Society Members' Ages
The video presents a problem involving the average age of 120 members of a society, which is 62.5 years. When 30 new members join, the average age becomes 58.2 years. The task is to find the average age of the newly joined members. The solution involves setting up an alligation grid, finding the differences, and using the ratio of the number of members to find the unknown average age.
Girls and Boys Average Weight Problem
A problem is presented where the average weight of girls and boys in a school are 30 and 36, respectively. If the number of girls is twice the number of boys, the goal is to find the average weight of the school. The alligation method is used, setting up the ratios and solving for the unknown average weight. The problem is also solved using basic methods to show an alternative approach.
Pass and Fail Students Average Marks
The video tackles a problem where the average marks of 132 students are 50, with pass students averaging 55 and fail students averaging 35. The objective is to find the ratio of total marks of pass students to total marks of fail students. The alligation method is used to find the ratio of pass to fail students, and then the total marks are calculated.
Family's Average Age Problem
A problem is presented where the average age of five children is 15 years, and the average age of the children with their parents is 25 years. Given that the father is four years older than the mother, the task is to find the mother's average age. The alligation method is used to find the combined age of the parents, and then the individual ages are determined.
Marks Scored by Students on a Test Result
The average marks scored by three students on a test result is 55. When two more students are added, the new average marks become reduced by five. The task is to find the marks scored by each of the two new students, given that one scored 15 marks more than the other. The alligation method is used to find the average marks of the new students, and then the individual scores are calculated.
Average Marks Attended by Students in Examination
The average marks attended by 120 students in an examination is 50. The average marks of passed students is 70 and the average marks of failed students is 30. The task is to find how many students passed the examination.
Average Weight of Apples in a Basket
The average weight of apples in a basket is 50 kg. Six new apples are added whose average weight is 60 kg, and the average weight of both together is 55 kg. The task is to find how many apples were there earlier.
Average Age of Six Members of a Family
The average age of six members of a family is 40 years. If the age of a guest is included, then the average age increased by 12.5. The task is to find the age of the guest.
Average Salary of the Employees in a Company
The average salary of the employees in a company is Rs 14000. The average salary of five technicians is Rs 18,000 and the average salary of the rest is Rs 12,000. The task is to find the total number of employees in the company.
Children Have Taken a Science Test
In class 10th, 40 children have taken a science test. 30 students give test and their score is 95 average score of 95 the other student had average score of 85. The task is to find the average score of the whole class.
Average Age of 10 Students and Their Class
The average age of 10 students and their class is 17 year. If the age of the class teacher is excluded the average age of 10 students is reduced by two. The task is to find the age of the class teacher.
Average Weight of Apples in a Basket is 50 kg
The average weight of apples in a basket is 50 kg. There are six more apples whose weight is 60 kg. The average weight of the basket is increased by 5 kg. The task is to find how many Apples were there earlier.
Average of 36 Numbers is 45
The average of 36 numbers is 45. Detected that 84 was misread as 48. The task is to find the actual average.
Average of the Marks of 25 Students in a Class is 19
The average of the marks of 25 students in a class is 19. The teacher realized that the marks of two students taken at the age of 18 and 19 Respectively instead of 14 and 15. The task is to find the correct average.
Marks Wise Wrongly Entered Age 65 Instead OF 45
Students Marks wise Wrongly Entered Age 65 Instead OF 45. The average of some of those kids is increasing by 1/3. The task is to find how many children do you have.
Average Weight of 32 Students is 70
The average weight of 32 students is 70 kg. The weight of the teacher is also Included. The Average Weight of the Class Became 17.5 kg. The task is to calculate the weight of the teacher.
Average of n Quantities is P and the Average of M
The average of n quantities is P and the average of M Quantities are Q. The task is to find the average of M + N.
Meaning of Three Numbers a / 3, b
The Meaning of Three Numbers a / 3, b and c / 3 is the same as the meaning of the number three. The task is to find the value of 3x.
Average Monthly Income of the Father and Mother
The average monthly income of the father and mother is 5000. The Average Monthly Income of Mother and Her sun is 6000. The Average Monthly Income of Father and his son is 10000. The task is to find the Monthly Income of The Father.
P is a College with 180 Students in it
P is a college with 180 students in it. The average marks of all is 88. There is Pay Q College here which has 320 students and the average marks of all is 72. The task is to find the average marks of Both the colleges of college together.
There are Seven Papers Carrying 100 Marks Each
There are seven papers carrying 100 marks each. There are three papers of Mathematics, two One is in English and two are in Hindi. He is getting 45 marks in Maths, 55 in English and 60-60 in Hindi. The task is to find the average.
There are Two Groups in Which Group A is Their
There are two groups in which group A is their The average weight is 12. which is B group Their average weight is 24. and the ratio is It is in 1:2. The task is to find their average.
Average of the Square Off
The Average of the Square Off The first five even natural numbers are. The task is to find the average.
Average Age of the Class of Six Girls
The Average Age of the Class of Six Girls is x. Four new girls have ages of x - 2 x + 4 x so much joins the class. The task is to find the New Average Age of the Girl.
Monthly Salary Which is Earning for 4 Months
2300 monthly salary which is Earning for 4 months. 1800 he earning for next 8 months. again 12400. He is saving so much money throughout the year. The task is to find the monthly salary.
They All Had 20 Marks
They all had 20 marks. The pass was 32 32 32 32. If two Numbers are so and so than what is The Average of the Remaining Numbers?
Average Weight of 49 Students
The average weight of 49 students in a class is 39. Seven of them whose average weight is 40 kg leaves the class. Seven more children are coming whose The average weight is 54. The task is to find the average weight of the remaining students.
Average of S Numbers is r to the Power of 4
The average of S numbers is r to the power of 4. the average of R The number is S to the power of 4. The task is to find the Average of R + S numbers.
Average Height of Three Kids is 56
The average height of three kids is 56. Their heights are in the Ratio of 7 8 9. The task is to find the height of all three.
Average Score of These English Exam of a Class of 49
The average score of these english exam of a class of 49 Students are in a coaching centre 52. A group of six boys having an average of Number 40 leaves the green class and another Group of eight boys having an average score OF 43 JOIN THE CLAUSE. The task is to find the new Average of the score.
Average Age of Ram and Shyam is 28
The average age of Ram and Shyam is 28 Year. If Rahim was replaced with Ram The average age of Rahim and Shyam is 26 goes. If Rahim is put in place of Shyam The average age of Ram and Rahim is 30 It comes. The task is to find the different ages.
Ram Shyam Rohan Rita and Mukesh Have Five Children
Ram Shyam Rohan Rita and Mukesh have five children. The average weight is increasing by two. The task is to find the weight of Ram and what is the weight of Mahesh and what is the difference in their weights.
Listing n Executive Even Numbers for Determining
While listing n Executive Even Numbers for Determining Their average, the Last Number by Mistake Got replaced by the next odd number and there by the average turns out to be more than the Desired value by 0 vo 0125. The task is to find the value of n.
Average of 12 Numbers is 25
The average of 12 numbers is 25. Each number is increased by 6. The task is to find the new average.
Student Number 72 Got 84 in Biology
Student number 72 got 84 in Biology, 91 in Hindi, 80 in this 73 Found it in English. The task is to find the average.
Average Age of a Group is Increased by 4 Years
The average age of a group is increased by 4 years when a Person whose age is 32 years was replaced. The task is to find the number of people in the group.
29 There are Boys and 21 Girls
29 There are Boys and 21 Girls. the average age of boys is 89 where as the average score of Girls is 91. The task is to find the average of whole Class.
Average of Nine Executive Odd Number is 27
The average of nine Executive odd number is 27. If The previous and next odd numbers to these Nine odd numbers are also included. The task is to find the new average.
10 are Consecutive Numbers Whose Average is Given By
10 are consecutive numbers whose average is given by which are the middle two numbers. The average is 13.5. The task is to find the sum of the six numbers.
Average of Six Executives Even
Average of Six Executives Even The number is 35. The task is to find the sum of the smallest and Largest even numbers among this six.
Average of First at Positive Even
The task is to find the average of first at positive even Numbers that are divisible by nine.
Average of Five Executives is Even
The average of five executives is even The numbers are at. If the The next five even numbers are also included. The task is to find the average of These 10 numbers.
Find the Average of the Cubes of First
The task is to find the Average of the Cubes of First Five natural number.
Average of Eight Executive Odd Numbers
The average of eight executive odd numbers is 48. The task is to find the sum of the fifth and seventh Number.
Average Of First Seven Non Zero Multiples of 17
The task is to find the Average Of First Seven Non Zero Multiples of 17.
Difference Between the Average of First 148 Even Positive Numbers
The task is to find the difference between the average of First 148 Even Positive Numbers and the Average of first 129 odd positive numbers.
Average of 11 Consecutive Numbers Positive Numbers
The Average of 11 Consecutive Numbers Positive Numbers Integers is d. If the last two numbers are Excluded. The task is to find the new average.
Average Age of Ram and Shyam is 28 Year
The average age of Ram and Shyam is 28 Year. If Rahim was replaced with Ram The average age of Rahim and Shyam is 26 goes. If Rahim is put in place of Shyam The average age of Ram and Rahim is 30 It comes. The task is to find the different ages.
Ram Shyam Rohan Rita and Mukesh Have Five Children
Ram Shyam Rohan Rita and Mukesh have five children. The average weight is increasing by two. The task is to find the weight of Ram and what is the weight of Mahesh and what is the difference in their weights.
Listing n Executive Even Numbers for Determining
While listing n Executive Even Numbers for Determining Their average, the Last Number by Mistake Got replaced by the next odd number and there by the average turns out to be more than the Desired value by 0 vo 0125. The task is to find the value of n.
Average Daily Production Of the Twice in a Factory
The Average Daily Production Of the twice in a factory in a month of December is 512. If the Average Product During first 20 days is 515 and the last 13 days is 510. The task is to find the average of products on 19 and 20.
Average of 18 Numbers is 65
The average of 18 numbers is 65 and the The average of first 10 numbers is 72 and The last 10 number is 58. The task is to find the average of the remaining numbers when we exclude number 10.
Average of 16 Numbers is 48
The average of 16 numbers is 48 The average of First Six Numbers is 45 and that's of the last seven Numbers is 53. The number six is six less than the fifth And five less than the seventh number. The task is to find the average of fifth and seventh numbers.
Average Age of Seven Students of a Class is 28 Years
The average age of seven students of a class is 28 years. Average of first three students is 30, The average of fourth student is four year less Then that's the age of the fifth student. The ages of The last two students are the same and five more are than that of average of first three Student. The task is to find the average age of the last two students.
Average of 12 Numbers is 42
The average of 12 numbers is 42. The last five numbers are 40. The first four number is 44. The number six is six less than the fifth And five less than the seventh number. The task is to find the average of fifth and seventh numbers.
A B C Starting a Business
A B C Starting a Business. The share of A twice the share of A means B has the same amount A has added twice as much and B is thrice the share of C means This means that whatever C has added, B has added the same amount Mixed three times. The task is to find how much of the profit did A give to A.
Three Partners in Which P, QR are Getting so Much Money
There are three partners in Which P, QR are getting so much money. P, Q, R are adding 1,000, 1,200 and 1,500. The task is to find what should be the share of Q if the total Profit is 666.
Kapil Initiated a Business with an Investment
Kapil initiated a business with an investment in April 2022. after 6 months his Kunal is my friend, he has joined. He has joined by investing this much money 6 months later. Then in February 2023, Kapil's who is ex class fellow oh saloni he is equal Whose amount did you pay? total Investment made by earlier to partner. The task is to find what ratio the profit Earn after 3 years.
Swati One Starting Up the Business
Swati one Starting up the business. She does it after investing ₹4200 which is after 5 months What happens, Bani joins Swati What is their profit after one year? That's 2:5. The task is to find how much did Bani contribute.
A, B, C are Telling Some Business
A, B, C are telling some business I am investing. Their ratio is this Is. After 5 months A invests another ₹4000. After 6 months, C Invests another ₹8,000. After 4 month, B withdraws ₹8,000. The task is to find after one year What will be their profit ratio.
X Y Z Enters Into a Partnership
X Y Z enters into a partnership. X Invest some money at the The beginning. Y inverts this amount of X After 4 Months and Z Invested Double the Amount of Y after 9 months from the The beginning. The task is to find what is the share of Y if the annual gain is 45.
P Invested 4000 for One Year
P Invested 4000 for one year q join him with an investment OFF ₹6000 after a few months. If at the end of one year the The ratio of profit of P and Q is 2:3. The task is to find after how many months did he go and get it mixed.
Three Partners a B C Started a Business
Three Partners a B C Started a Business by Investing so much each after 5 months a left the business After 9 Months Be Left The Business And After 12 Months See Left The Business. If the total Earn is this much. The task is to find the share of C is what Percent more than that of B.
Mohit, Rohit and Ayush are Some
Mohit, Rohit and Ayush are Some Starting up a business. Mohit Whose Money has been used for 5 months and My profit is 1/16. Rohit Whose money is being used for 4 months. He is saying that my profit is 1/3. Ayush head invested this much for 10 Months. The task is to find how much money did mohit and Rohit contributes respectfully.
A B There are Partners Who Invest Money in a Business
A B There are Partners Who Invest Money in a Business. A is 1/th of the Capital. For 15 months He is investing. B gets 2/3 profit. The task is to find for how many months did B work.
A B C Starting a Business
A B C Starting a Business. The ratio is 6:5:4. After four months A double the money. The task is to find the Share of C if the profit is 23100.
