COMPLETE ARITHMETIC MATHS - PART 3 | SSC EXAMS 2025 | MATHS MANIA

0:10 So today we are going to study the average which we It is also called average. So if the average of If I talk about the basic concept then suppose If I have to find out the average salary. 20 people What am I doing with a salary of Rs 20? I am adding it. Whatever 20 people there are, all of them I am adding the salary and giving it 20% I will divide it by . because there There are 20 people so I divide by 20 I will give it. So this will be my average Salary. That means the average salary everyone has is So much has come that on dividing me, The value has come. Ok? or you think like this You could say that I have taken everybody's salary in my hand I took them in and treated them all equally Distributed it. So I divided it equally isn't it, we will get the same amount which is divided equally Everage says. Ok? so this is the basic There is a concept that I hope you know will be. Ok? so the allegation is here It is written because the first problem we deal with who are going to deal with the first types

0:56 We are going to answer all the questions from the allegation Will apply. So if you know the concept of alligation If you don't know then don't worry Is. I will tell you where the allegation is But we will apply it. Ok? so there we are alleging Where we find a hole Somehow there are some people or whatever Can. There are some people, I know them only on an average Is. Isn't it? I know the average. along with that A piece of every person is I know the average of the share. and the one who survives I know the average of that part. From us He asks whether there is any difference between these two men here. Either you can ask about the ratio or you can ask anything that how many men are there or how many in both They are men, I know their ratio, ask me anything Can. So we have to put the alligation there Where I know the average of the total part. know the average of one part of it and the remaining His average portion got lost which was left over You should know its average share. for example

1:42 Example: I will give you a very good example. I will give it. Like some children in class 10th Are. Class 10th first thing in two parts It is divided into section A and section B. So The class 10th student is telling me this Whichever is Section A or Section B, both Including the total number of students in class 10th His average age is, suppose that he Your age is 17. of class 10 students who His age is 17. but what he is telling me is Section A's average is 19. The average of the children in section A His age is 19. and those in section B The average age of the children is 16. No section Here is section A. section B here Is. Average age of section A is given. Section The average age of B is given. and section A and Combining section B we get the average age here I have paid it. So what do we have here? These

2:28 Look, we have been given a share. these others I have given my share. got both parts has given it. So I'll understand here, brother. My question will be answered due to pay allegation. well what I am saying is there You can also have simple interest. Some? It also means like this. which I give you I have already got the questions done. Simple Mix allegation in interest etc. I have already done it for you. Ok? Ok? Now what does the question ask us? that the number of children A and B have to me tell me what are you tell me their ratio How many children do you have? as many children as Tell me the ratio of A and B sections In. So simply what do we do? First The thing is you have to understand that this value Is there anything in between these two It will bring value. You must understand this It is just that. Ok? between these two Went. So what do we do? which is the bigger one The value remains as you see 19 It is big. So after subtracting 17 from 19 we get here I will write it on it. So come here.

3:14 Then we subtract 16 from 17 and we get I went here. Look, once I went from here I reduced it here because this is a big one The value is in the middle and this one is small. Then We subtracted here from here and got this. This is why it is important for you to understand this direction No? because sometimes we feel like here There are 19 diyas here There are 16 diyas here But I have to accept x. Isn't it? so me One thing to understand is that I am 16 - x here or should I write x - 16. This confuses me Might be possible. So you have to understand this, look at this Among 19 and 16, 19 is greater. So from here you If you minus this, you will write 19 - x here. And here you would write x - 16. 16 - x votes Write it down otherwise your answer will not come. so I am telling you the direction. You You can take any direction. either Take it like this and walk like this. anyhow Let's go but you have to walk like this or else walk like this Either you have to walk like this and like that. Understanding

4:00 Went? Ok? Ok? so what I was supposed to tell you was that the section The number of children in section A and section B What is the ratio? So what did I do? I minus this from this and put it here to I wrote it down and after minusing it, put it here I wrote one. So this one and two come has been in the same ratio as section A and Children of section B are divided in this ratio Will be. Meaning in section A if suppose if There are total 30 children. If that was given to me If you have total 30 students in class 10th then There will be 10 here and 20 here. will go because their ratio is 1:2 and this Your 10 and 20 together make 30. Correct Is? So now let's look at the next question. very wonderful very good We will see. Understand very carefully. Look at the The average age of 120 members of a society is This much. Means 120 people who are in the society His average age is this much. Bye

4:45 addition of 30 new members 30 new members If they go then the average age becomes that It becomes 58.2. so what is the average age Of newly joined member. Ok? So we How will we understand here that we have to make an allegation Have to apply it. So you have to understand that I 120 is given for the member and then 120 more plus It is given by 30 members. Ok? 120 and 130 It is given by the member. So much edge. So this is the total It happened to the people. It became one and one I don't know but something like that is happening here The discussion is going on. 30 people have come for them The discussion is going on. Ok? So we give him the same I will write it in this manner. Understand? so be careful See how to do it. Look at me from here You will understand that I have to make an allegation. Because he is talking about some total. Some? People are talking about 120 people here. Here I am talking about 30 people. Now Look carefully. We are talking about 120 people here.

5:32 Used to be. I am talking about 30 people here. And here we are talking about the average of 150 people Used to be. Ok? so 120 120 people who are His average age is 62.5. and look at this 30 people were added so now there are 150 people Have gone. So the average age has become this much. So That means the average age of these 150 people is this much and I assumed this to be the average age of 30 people x Is. I accepted this much. Now if I use this If I see the difference here then the difference It is coming, I see it is 4.3. here 4.3 is visible and here I tell you hai, I minus it like this, so I did it like this If I minus it, I get 58.2 - x here. It will be visible. Now this ratio which has come out is The ratio has come, you need to understand this. Whose ratio is this? who was formerly a member 120 and these 30 members who came later. of these So this is the average because I got this 62.5

6:19 The average given is of 120 and this one is of 30 x is the average, this is given by 30 people. so this The ratio that I have come up with is from these two people It has been found that this is a ratio of 120 and 130 only The ratio that you are seeing is 4:1. So This is your 4:1. Ratio of 120 and 130 If you take it out, it will be 4 1. Ok? So now You have to look carefully. Look at this from the forest If I turn it into 4.3 then it will come out to be 4.3. So this Even if I multiply it by 4.3 is coming up. So if I multiply this If I give you this 4 * 3 = 12, I got one 4 16 one will give 17.2 whose value is 58.2 - x Is. So from here I can calculate the value of x very I can easily extract what you are seeing It is one and you are seeing four. 41 showing is the value of x. So there were 30 people here His average age will be 41. Understanding

7:06 Went? See the next question. to you even better Things will make sense. dekho in a school The average weight of girls and boys are 30 and 36 Well, we can do this with basics also. You can do it with basics also. But I'll let you I am showing it to him also. from his basic We will do it too. Ok? so look what else you say Used to be? if the number of girls is twice the Number of boys than what is the average weight Of the school. Ok? so he is telling me The average age of the girls is 30. 30 And the average age of the boys is 36. And I don't have an average age of both combined. has given it. I'll take this to be x. Correct Is? Now you know the larger value is 36 So 36 - x I'll write it here and here I'll write x - 30. So what is this? These Your ratio of girls vs boys has arrived Ratio of boys. If I were to talk to girls and boys

7:51 If I calculate the ratio of , this is what we will get. This is what will come. and gave me its value that the number of girls is twice the number Of boys. So there are two girls and two boys There is one. So from here, if I solve this Look, 36 - x = 2x - how much will you get? 60 then what will be the value of your 3x Will she go? 96 will come. So your value of x is How much did it cost? 32 has arrived. so from here 32 is mine The correct answer has come. Understand? so do it like this Are. I am telling you again. here I was given the average of the girls. here I was given the average of the boys. here The average of both was given. so me From here it became clear that these girls and boys What will be the average of? then girls and boys The average will be this much. And I know this The average is 2 / 1. So from here I can calculate the value of x I can find out the value. Now to do this A very easy way is to do this directly Do it from the basics. See. So here you know that the girls who

8:38 Her number is double that of the boys. So you assume two girls and one girl Take. You can assume that, no problem Is. So I thought there were two girls. So the age of both the girls should be this much Will go. If there is a boy then his average age means Whatever his age sum will be, this much. And how many people are there in total? two girls one There are total three boys. so if 60 36 96 / 32 So your method is easy. But let me teach you the method of alligation what then? We also do this. Ok? So I hope you have understood. Let's move ahead. Dekho average age of 132 students of a college is 50, if the average The age of the marks of the pass students is 55 AND THE AVERAGE OF THE MARKS THE FAILED Student is 35. Ok? So you carefully See. How did I find out about the allegation here? put it because I know that the kids who The average marks of those who passed

9:24 His marks are 55. the children who failed His average marks is 35 and he The total number of children born including pass and fail His average marks are 50. So from here I found out the difference between pass and fail What is the ratio? which is 3:1 to me It is visible. these kids are nearby and these kids I have failed. I got this ratio. But What ratio have you asked me about? Attention Look from. What Will Be the Respective Ratio of the total marks of the pass Students and Total Marks of the Field Students? that the total pass and total fail of the students What is the ratio? I mean sorry their marks What is the ratio of? so look at you here look here, here, by the way, if you Do you want me to tell you how many people are there who have Has happened. How many people have failed? By the way It's none of his business but I'll tell you I have been. So you know there are total 132 people

10:10 Student. you know if this 3:4 came then this are those who passed or those who failed then total if If you do this then it becomes four and the sum of that four If the value given to you is 132 then you need to key one The value is coming out to be 33, so what you have to do The children who passed will get a value of 99 And the value of these is 33, the value of one is 33. If it is okay then it's okay and if this one fails If their value comes to 33 then this is yours okay so he is telling us what will B The Respective Ratio of the Total Marks Passed by Student and the Total Marks Of the field students means those children who pass whatever their numbers are, their total should be made even Give two more children who have failed, all those children Make the number of even. So the ratio that is coming Please tell me that ratio. then 99 people If the ratio of average is 55 then divide it by 99 * 55 Give. And you have to tell me this ratio which is failing

10:55 33 people failed, their average marks are If she is 35 then I will make it 33 * 35. Ok? Now You see here, it is going on three times. Is. And it was 3:1. Now I am direct from 3:1 I could have done it too. I can do this completely too or I could have done it by taking their ratio Was. There was no problem with that. Ok? So From here you subtract 11 from it. from five Cut it out, sorry. So this is your seven. So That means 33 is seven. What? What has come? marks of these children who passed and Ratio of marks of students who failed has come. Meaning of total marks. Marks That means the ratio of total marks has come. Correct Is? Let's see the next question. the average of A Family of Five Children is 15 years old. Average age of child together with there. Well, these are the questions that I am telling you yes you can do this very basic thing as well

11:41 You can, but I am telling you the allegation Because you will get a lot of questions from alligation. It happens quickly. But sometimes when the data Like a lot of data is easy when Much more than your basics goes. But when the data is slightly reversed If he gives it directly then it will be easier for you than alleging It happens. Ok? So I'll just give you an allegation I am teaching you because you are from the basics You will do it too. I will teach you the rest I will tell you how to do it from the basics. Ok? Look at the average age of five children of a Family is 15 years old. Average Age of Children Together with their father and mother is 25 years. If the father is older than the mother by four years Then find the average age of mother. how to you You will understand that an alligation has to be made here. Look at the alligation, how do you know that The average age of five children is 15. And when both his mother and father If we include it then the average age is

12:28 It is 25. Look here, look at the five kids The average age is 15. and when his parents If you include it then your average age is 25 It happens. so here basically I Their mother and father were included. Father Mother is included here. here All are children. There are five people here. There are two people here. and I get the total of these Together they have given me an average. of these five The average is given. total ka diya and these two of which I accepted FM. x assume anything Accept it. Isn't it? fmn I accepted it as my father Mother agreed. Ok? what are you saying now? Now what will I get from here? me here From this ratio you will know how many children And how many moms and dads are there? Ok? So Well I know, but write it down here. to the thing. so here this 10 comes and look at you here you know that this The value is small. This one is in the middle, this one The value will be large. Means here I have FM - I have to write 25 and here I have to write 25 - 15

13:14 that comes to 10. Ok? Now one thing you Tell me what the ratio will be Is? These are kids, and these are mom and dad. So the ratio of the number of members is what will come? I know there are five There were children. and here I know that here How many people were there? There were two people here. There are only two people, mom and dad. so here There were two people. So you are seeing this 2 * 5 It has happened. So this will also become 5 * 5. whose The value will be this much. means the value of 25 which is coming fm If it is coming to -25 then what is the value of FM? 50 So what is this 50 you got? It came to you that Mother Mother The average age of mother and father is 50. Ok? So now you can see that the mother His age is four years less, right? If the Father Age Father is 4 years older. so you see mother's age will be 58 and father's

14:01 Age will become 52. so you can remove it from here yes. Who asked you? I have asked about my mother. You asked about your mother, right? So tell the age of the mother. So your mother's age becomes 48. Understand? This was also an easy question. See. The Average Marks scored by three students on a Test result is 55. Ok? when the two more Students added, the new average marks Became reduced by five. Ok? So now Let's see what he is saying. Look at the three people The average age of is 55. When we add two more people If you do this then your average age is five It is being cut. Meaning it is going to be 50. So If I added two people here then it means here There were some people there, there were three people, right? Sir. There were three people and two people were here I added it. Meaning their average age That's it. Their average is this much and the total The average age is this much. So from here, if I If I take it then you can see that 55 is bigger. These

14:46 It is small. So here what would happen is 50 - x It will happen and here you will get five. And You already know the ratio, there are three There were people. There were two people here. So you look at this What is 2 * 5? So what is 2 * 5? Sorry no what has into 2.5 done? so here If you convert it into 2.5 then you will get 7.5 here. Will go. The value of 7.5 is 50 I gave you x Is. So the value of x that you will get is How much will you get? It will come to 42.5. So Here I have to calculate the value of x which is given by both the people two kids had come, two more students who a and b came, their average age is 42.5 will come. So if I open the edges of both Let me take the total edge. The sum average of these two What is the sum of age? So this is done in two steps I will multiply it. So your score will be 85. This will be the same age as both of them. tell us now It seems B scored 15 marks more

15:34 are from A. So how much did both of them score? So whenever you get a question like this, just simply answer 15 Take it out first because 15 are more or Anything less, you take out 15. 15 If it was too much then I took out 15. Whatever is left I will divide it equally Am. So how much did I save? my 70 escape If I go then I will divide it between them 35-35. then 35 This is done and it will become 35 + 15 which is You will become 50. Ok? so what about us Ask 35 and 15 your option has come. 35 and 50 What happened to you? Both A and B have their own Marx has arrived. what are you asking us? A Of. So you know a is less so a has 35 Will be done. Ok? See the next question. The average age well you are getting it Not that why are you making allegations against us? because look what we have here like There were three boys. I know the average age of all three

16:19 Was. Now two more children come. whose I don't know the average age so I took the x value Took it. Their average age is x. by the way here We were talking about Marx. Average Marks is x. Now when both of them come, it means These three and these two together give me an average of five I found out the age. so look at me know this age Is. I have accepted it and I Do you know. And I know the ratio. Me I already knew the ratio, this is three and this is two Is. So the way we write it is By writing it in the same way, whatever other value we get I don't know, we have solved it. As What to see here: The Average Marks attended by 120 students in n Examination is 50. So what about 120 people? The average is 50. if the average is an average Marks of Passed Student is 70. Who The children who passed, their average is 70. Sorry The average marks are 70. and the kids who failed His average marks are 30. so me

17:04 Look fail pass total is just that easy. pass 70 fail 30 is 50 of the total. so from here i I saw your 20, 20 and 20 here. will be which I can also consider as 1:1. So Meaning, equal number of children have passed. Equal Only the children have failed and if there are 120 children then 60 of yours might have passed and 60 might have failed. So he is asking us how many marks did we pass? So Only 60 have passed, only 60 have failed. Ok? The The average weight of apples in a basket is 50 Kg. Ok? The average edge in the basket That is 50 kg. Now we have brought six new Apple Whose average age was 60. Ok? Look, it's 50 now. I bought six new Apple Included in that. His average age was 60. Now What is the average age of both of them together?

17:50 Done? That's your 45 now. Why? Sorry it's 55. Why? because by this he If I increased it by five then it became 55. So Look at the average age of all the Apple devices that were there earlier. A sorry friend, why am I only saying average age In the beginning I was an example of average age If you take it then it will be an average age here it's ok there is no problem with it The average weight is 50 and the one which comes after six I added more apples and their average weight is 60 and the average of both together is His weight is 55. So you can see it from here You are seeing 1:1. I have given you here you know i did six apple ads i mean I did it into six. so here maybe first I will into six whatever apples there are. So I already had six apples. Six Apple I did the latter. so here there are six Asked. I asked you how many Apples were there earlier? Six Apple was the first. Ok? Now see what you say Used to be.

18:36 The Average Age of Six Members of a Family It is 40 years. If the age of a guest is included, then the average age increased by 12.5, What is the age of the guest? would have done it He also has it. We can do this also through allegation We give it. many more ways many more ways Are. Right now we are learning alligation. look at this There were six people and their average was 40. New one A guest has come. I assumed his average age to be taken is x. Now the new guest who has come and who These people were already the complete average of these people If I add their ages then what is their average age? Is it being made? He is saying that the average age is 12.5 It is increasing. means 1/8 It is increasing. then what is 1/8 of 40 It will be 5, which means their average age will become 45. So you see it has come here five has come here Went. Look at you, let me tell you one thing. 45 here - Will you write x or will you write x - 45. its decision how will you do it? so you know since 40 this

19:23 The value is small if it is in this direction Must have gone. Meaning, five has been subtracted from 45. So from here I'm going to minus 45 from x. So I'll minus 45 from x. There is no in this Don't get confused either. Ok. now from me what are you saying? ok tell me one thing. We I know the ratio that will come out You must know first how much ratio is coming There were six people and here one man said it is 6:1 So this is into five so this is also into If it becomes five then this is basically 30 for you. If you have given this much value of 30 then your x What will be the value of 45 + 30 75 If you go then you will get 75% answer because he is asking you that this man who came Next, its average age is also this much Why would its actual age be this much? Because he is the only man. So it came to 75 The age of this man. He has asked us about our interest What is the age of? Ok? I hope

20:08 You must have understood it very well. But let me ask you a couple more questions I have been. Ok? So let's do it quickly. average salary of the Employees in a company are so many. The Average Salary of five technician is this much and the The average salary of the rest is this much. so me Look, I know this thing that the total of all The average salary of employees is Rs 14000 Is. The average of the technicians The salary is Rs 18,000 and those who are saved, The average is this much. so what do I do from here I do, I take the difference. so here From here I saw the difference 800 and from here The difference I saw was of Rs 4000 Went. I saw 1:5. He was a technician. These were other employees. so I know These technicians were five in number, meaning into

20:54 I gave it a five, so I gave it a five too I will do it, the other members will become 25 If you have asked me the total then 25 + 5 = 30 so 30 My answer will be correct, it's ok There is an option here, friend, these people can get even 25 I should give you 25 and also one five I should also give it okay okay let's talk no yes look there is 40 in class 10th Children have taken a science test which is science 30 students give test and their score is 10 average score of 95 the other student had n Average score of 85. what is the average Score of the whole class? I allege this I will not do it because the value is enough for me Eazy is looking. You need more than allegations It will be tough too. So we do it from the basics Are. I am telling you with allegation how do. so by allegation i know 30

21:39 The average score of the children is 95. and who There are 10 other children, their average score is 85 So here I will assume X. so here I it will be visible on 90 - x i can see it here will go to 8 not x - 85 and I will find their ratio I know because you see here, 30 The average score of the children was 95 So this is your 30 and this is your 10 so you can also write 3 1 so you know no, if you write it here simply like this 3 / 1 then you can solve it from here Your answer will come but here we are telling you we won't do it, right, basically simply what do? look the first thing you need one thing and I Let me explain. Whenever you calculate the average age like this If so, what should we do? we us this

22:27 So what you have to do is make everyone's average age even He has n number of people than him Divide it. So there are 30 students here. and here you have 10 students who Those who survived became 10. there are 10 now It must have been given by the students because those who survived. 30 rupees he gave me this much and 10 rupees he gave me I have given so much. So I took its ratio also I can. You should consider it as 3:1 that three The age of the people is this much, the average score and the one who This is his average score. So you look at 30 * 95 plus 1 * 85 divide by how much tax Shall I give it? I will divide it by four Because three and one become four. so you here Find its answer from this. yours comes easily The answer will be given. Ok? look at the next question Are. The average age of 10 students and their class is 17 year and their class teacher I am 17 years old. If the age of the class teacher is

23:14 Excluded the average age of 10 students is Reduce by two. Ok? So you look very This is a wonderful question. very carefully now Understand how we can make the allegation? Find a solution for this. Look at the total of me given who are the children and who are the class teachers His average age is 70, I have given it to him. And He is telling us that if the teacher is removed let's go. Isn't it? Suppose teacher's x happened. because the teacher and the 10 children are 10 You have kids, right? Including their 10 children If the average age is so much then I respect the teacher taken is x. now he is saying when the kids If the teacher is removed then he will take the average The average age of the children that is coming, the average age What are you talking about? it's decreasing by two Meaning it is going to become 15 from 17. so this You have 10 children. So you can take it from here Take. So you know it's happening 17 - 15. So you would write x - 17 here. Because these It is going in this direction. So you It has to be written in this direction. Then, x-

24:00 You will write 17. You will write two here. and you get a There is one more thing I have to tell. Here is the ratio. These Whose ratio has come? How many kids here And you know how many teachers there are here There is only one teacher and there are 10 children. So It is coming at 10:1 brother. that's all Used to be. So this happened into two, then two came Is. So if you do this into two then you will get 20 It will come whose value is given by you. So 20 = x - 70 then what is the value of x for you Have you arrived? 37 has arrived. So you can do it like this. Correct Is? So I'll ask you this question I am telling you how to do it in a basic way Am. Ok? Look what we do? Look what we do Are? basically thinking in this way that this I have given them an average age, just consider it a toffee

24:47 Everybody has it. Isn't it? All of them have toffees. There are so many toffees. Toffee example I find it very best. so I I am telling you it is toffee. so it is saying that they have 10 kids and one teacher who Those are toffees, everyone has those 17 toffees. everybody's age It is 17. Understand this to mean that there are 17 toffees all have. If the teacher has a teacher who If this is removed, then the children who have one child each The toffees that a man has become 15 toffees. This is saying that 15 decreases by two. then give The toffee decreases. That means there would be 15-15 toffees Is. So look, look carefully. these 10 You have children, right? These are your 10 children. Their Everybody has 15 toffees each Is. But if we include the teacher in this I will give it to you if you include a teacher If I do it, all these people will have toffees She goes and becomes 17 17. well like that

25:34 Why is this happening? This is why it is happening Because we have taken average here. We what did you do that you grabbed everyone's toffee and got into everyone's Distributed it. So now everyone has 17 toffees each Are. But initially there are 15-15 toffees. So this means that the teacher who has come He had too many toffees. which to everyone If he distributed it equally, everybody would have it It will be 17. Ok? So I accepted it because when we met our new teacher The average toffee is 17. So I assumed The teacher must have at least 17 toffees. The extra toffee that comes with it is the same He distributed the toffees among everyone. So Plus, you can assume that it will have more X toffees. It has 17 toffees plus there will be x more toffees. Ok? And this is the X-Toffee he has He gave two toffees to everyone. Everyone has it 15-1 is the toffee. So he gave two toffees to everyone. Must have given it. So everyone now has 17 toffees. Everyone has 17 toffees. It's fine now? So this He must have given two toffees each to only 10 people.

26:20 That's why brother if everyone here has 15 toffees Are. If there are 10 people, then give two coins to each of them If you give me a toffee, now look everyone has 17-1 toffee Everybody has it. So you know if If he gives two toffees each to 10 people then his There must be 20 more toffees left. means 17 toffees So it has it. along with these 20 toffees and Should be. That's why these 20 toffees were given to all of them will be able to share. So it means that the one who has the toffee That would be a 17 + 20 toffee. Meaning 37 There will be toffee. After this, I mean its age which is He is 37. I took the toffee so that It's easier to explain it to you a little. Little You might be feeling awkward, strange will be. But it will be easy for you to explain. That's why I took your toffee example. Took it. Ok? So this is a question I'm asking you And I am getting it done from the basics. Isn't it? His After that we will move on to the next type. So telling me the average weight of apples In a basket is 50 kg. means a basket

27:08 which I am drawing with such lines Am. Isn't it? So from here to here Apple I assumed that from here to here I have kept such apples till now. I assume so I will take it. I draw lines like this I will take it. It's easier for me like this Draw a line. So you should also learn this if If you need help then it is available. Ok? so here All the apples that are kept from here to here The weight is 50 kg. way too much Let's take some practical questions here Are. How can an apple weigh 50 kg? could it? There is no problem here. So Everyone's weight is 50 kg. what have I done now? There are six more apples whose weight is 60 kg. Correct Is? So, please buy this Apple for us It will happen brother. There is a 60 kg apple. One no problem Is. So here are the six apples of these six The weight of these six is ​​60 60 60. By the way You know this is about average age Is. But I assume that everyone

27:54 60 60 60 60. Ok? then it is average It will also become 60. Ok? Everyone's 60 60 60 Is. now telling us the average weight of the Basket is increased by 5 kg. means if I will take the whole thing when I add these six Whose average weight was 60. So now these The average weight of everyone has become 55. So How has it become 55? because these six 60 means this is their average weight More is more. more of the same everything It is equally distributed. So Everyone has reached 55. You can also eat it like a toffee Please consider it. What does toffee mean? for everyone There were 50-50 toffees. here with everybody There were 60-60 toffees. Now everyone has 55 toffees each Went. Meaning everyone now has 55 toffees each Is. So how is 55 55 Toffee? look at you You know there are six people here. Here I am

28:39 I made it so that all of them had 55 I gave 55 toffees to all of them. I a little bit of this Let me write 60 on top. So I divided all of these into 55 Gave 55 toffees. Give 55 toffees each to six people Gave. So you can see now five of them all. Toffee is being made. Look at all of these Panchap How many toffees will be left? There are six people. One People have five toffees extra. So total 30 There is extra toffee. Now these 30 extra There is a toffee in it, that is distributed in it. which from here There were people even here. it is divided in it only then these whole The average came to 55. Okay, how did 55 come? Look, I have made them 55 55 55. Now These too have to be made 55:55, after all everyone This is the average, then it will become 55. This is what happened. So I am distributing those 30 extra toffees Am. And how much am I sharing with you? Tell me. When everyone here is 50-50. 50-50

29:25 Everyone has toffee. So to everyone I I am distributing five-penny toffees. and i have There are 30 toffees, how many should I distribute? will I be able to I am distributing five-poffies to everyone. So I will distribute the fifth topic to only six people. I will find it. I mean here what is here is six I only had Apple. Ok? i you I am explaining it one more time. very attentive You can understand from this. I have some apples from here to here Whose average weight is 50 kg. Then I added six new apples. whose His average weight is 60 kg. so you see It is being said that these 50 to 20 thousand rupees and everyone has got this whole The average weight of is 55 kg. So I what did I do with all this if I accepted 55 then my How much extra is left? out of all Five-five extras are remaining. Meaning 6 * 5 = 30 extras are left. and this Which is 30. 30 I will distribute them, but I How much am I giving to each person here?

30:11 Because from here everyone's average became 55. Meaning this should also be 55 55. They also get 55 55 It will have to happen. So I mean I give five to everyone I am giving it to you. So how many should I give five five can I give it Because I want to win by five I can give you five, that many people are here Are. So I am giving everyone a 50p. So six I will give people 5-5. means here When I give five rupees each to six people then Now everyone is 55. my average age is complete 55 has arrived. So there are only six people here. Will be. So it will be six apples. one thing i Let me tell you more. So this is mine Answer. This is the basic way we will do it. Ok? However there is also a more basic method which We will multiply our total by doing just that. I will not tell you the way to do it I will find it. Are you understanding? That method is very Meaning you shouldn’t do it. Ok? Now one more thing Know it. I want to tell you one more thing here Let me observe it. Whenever you need something

31:01 Average weight should be given for so many people. here Average weight of so many people should be given. and here But if the mid point comes by mistake. both of these the mid point of came here if I There will be equal number of people at both places. Like look here, whatever was yours earlier It was 50. What was new, you added Apple His was 60 and both together make 55 Went. So look, this is the mid point. So As many apples as there are here As many apples as there are here There will be as many apples here as there are. so here is six If there were apples then there would be six apples here too. We asked one more such question which I will tell you about I am showing it to you once. I asked one question about 7030. Yes Look what is there here? Look here The average of those who passed was 70 Was. Those who failed, their score was 30 and the total

31:49 He had this much, 50. So you see this is 70 30 The mid point is coming to 50. Understood? Because This is for total. So the total that is coming is The midpoint is approaching. So, the number of children As many children who passed will also fail. Ok? So now let's move on to the next type. Ok? So, we have seen a lot till now. Is No? I am telling you one more thing. Basically I will make it clear to you one more time I will give it. What does average mean? That There is nothing that is equal among all of us We are distributing it. just understand that because We have to find the answer here. So all of us I am distributing it absolutely equally Are. there is anything and I told you everything Everyone has equal rights. So the value which Any one person will have whatever value Whatever it will be, that will be my average. Are you understanding? This is how we ask questions. everyone is mine The motive is that we should treat everyone equally Have to distribute. to divide them equally

32:35 The methods can be very different. Correct Is? So understand this very carefully. Look Attention what are you saying that the one with 36 numbers The average is 45. Meaning there are 36 numbers. Everyone has 45 45 45 45 value. Sabki 45 The value is 45. Ok? letter is what Detected that 84 was misread as 48. Its What does it mean? that later I came to know that the 84 Was 84 is wrongly read as 48. Meaning you had a number 84 you accidentally I read it as 48. Ok? means you have some Counted less. Ok? so how much did you Did you count? You counted 36 less from here have done it. Ok? Meaning you get 36 values ​​and

33:21 you should have taken it but now you have taken 36 36 value You have taken less because of which your average is higher than everyone else's I got 45 out of 45. now saying that if you If you had not read it wrongly then the original would have been the actual average they average your average should come that How much does it cost? ok tell me one thing now The pass is 45 45. And what did I tell you? Everything has to be distributed equally to everyone Some. Everyone has equal distribution You have to give it. means you have some supposition Do you have money or something, everybody has toffees You have to distribute it equally. So you are like this Think I counted 36 toffees less. Are you understanding? I counted 36 candies less Was. So if I don't count 36 toffees So what is the average here? this is what I ask you Used to be. So if you don't count 36 You should treat these 36 equally as well I would distribute it among everyone. So if you

34:07 If we distribute equally among all, how much will one get? Would I get it? You know there are total 36 people and 36 If there were toffees, everyone would have got one more toffee. So your average age would become 45 to 46. So That is your ans. 45 becomes your 46 Will go. That is your ans. next question Look, you will understand it better. See saying the average of the marks of 25 The number of students in a class is 19. means all 25 All the children's numbers are also 19 199 19. Well I thought it was not actual Is. I assumed that everybody had 191 Everybody has a number. now he is telling us these An examination was calculated to be 19. let the teacher realize that the marks of two Students taken at the age of 18 and 19 Respectively instead of 14 and 15. Its What does it mean? there were two children who

34:54 The numbers were 14 and 15. It was 14 and 15. But I accidentally gave him his number 18 and 19 were counted. means I I have counted too much. because of this here The pay value must be higher. else x's The value should have been a little lower. This talk You are understanding it, right? because I've Their number was counted more by mistake Is. So here because of this this value I will get more because if I am actually right If he counted 14 15 then it is obvious Its value would have been a little less. to everyone I would get a little less. So you look here +4 here and +4 here means I have given the total I have counted eight extra. Ok? Well, I counted eight too many. Then this is mine coming. so what should i do Will it need? to take something out of it all Will have to take it out. The eight is the total value No, I will take a little bit from everything So my total value will be eight. So

35:40 You know, out of these 25 people, eight each If you want to find the value then divide it by 25 Will you give? Well this would be a minus because you I counted too much. Counting you less If you want it. Just accept anything like that Take it, let it remain at eight, then you have it here what will happen to you 32 so now out of all of you Find 3232 because you need these eight numbers. You have to take out these eight from this whole You have to find out the number, understand number eight and this This is an average, also keep this in mind, this is an average So we are taking out eight out of all like this Count out eight so that out of all of you If you take out 32 32 then it will be 3232 then your eight If it comes out then you will get only 0.32% from it If you want to minus it then it is yours because you are a Which one of them takes out 32 from each child You are one of every child and one of the children, aren't you? If it is 19 then your result will be 18.68 so this

36:27 Your correct answer is 18.68. Ok? See the next question. Look at us students Marks wise Wrongly Entered Age 65 Instead OF 45. Ok? some kid is telling The number was 45. but by mistake 65 I wrote it there. I have written 65. Ok? because of which what happened to everyone ok tell me one thing this number 20 An extra amount has come which is 20 numbers extra Here comes you see the average of some of those kids There must be a child whose number I have given 20 If you count more then it is 20 There was an extra count by mistake, that's all It would be divided equally among all So this will be 20 numbers when n numbers are off in all If it gets divided among the people then this is number 20 Because of this your share in all is 1/3 1/3 1/3 The number is increasing because of this number 20

37:13 So number 20 when there are n people with son then everyone If i increases by 1/3 then the value of n The number of people will become 60. So the question is how many children do you have? Ok? dekho the average weight of 32 students is 70 It is kg, right? 70 kg the weight of the teacher is also Included. The Average Weight of the Class Became 17.5 kg calculate the weight of the teacher. By the way You should do this by alligation and tell the answer. Tell me the answer by alligation. The rest of this I I am telling you how to do it also. This How to do it the right way? look carefully at you See. Look carefully. very carefully Look I know I treat everyone equally I am giving it. You are understanding this Isn't it? Look, there are 32 children. from here to here There are 32 children till now whose average weight is

38:00 yes he is 70. if the wait of teacher is also Included. I did not assume that the I have included the teacher. I would assume that Am. This is the teacher I included First of all, there is a teacher who also has weight That's going to be 70 plus something plus x will be. Why? because average weight increases It is happening. So brother this is the extra one The average weight is because of the extra It is increasing. Ok? So I Simply assume that its average weight is 70 + x will be. Ok? Now the average person who is telling us His weight is now going to be 17.5. means this Look at everyone here, everyone's average weight is 70 Is. The average weight of all is 70. from here to here The average weight of all the people till now is 70 70 It is 70 70 70 70. Everyone's teacher also has 70. But now this Top 5 is all in and but going. And how many people are here? 3300

38:46 There are people. Isn't it? well then 0.5 in all butt Used to be. For what reason is it divided? Because its The teacher's average is 70 + x. so what is x This is the reason why our value is there in everything This x will be divided among all How much is the butt coming in everything equally this is top 5 butt how many people have five butt There are total 33 people because they call themselves also giving some wait now because Everybody has reached 175 now, which means I have also reached 175. I have given you a five and I am giving five to everyone else. Whatever be his condition in giving fives to 33 people how much will it be make it how much It will be done, if you halve it then it will be yours It will become 16.5 so this 16.5 is the sum of x This is the value. So your result is 86.5 from here. The average weight of that teacher will be given. this I give you I am telling you by drawing. In this you will find a lot

39:32 It will take very little time if you can think like this So. Ok? Look, the average of n Quantities is P and the average of M Quantities are Q. tell me average M + N Telling the quantity. so I know. Look, P is of N people, so the total is this much Will be done. If Q of M people is then total is this much Will be done. Look what I said that the average of n quantities is p means everybody has p of n quantities so I If you calculate the total then the total will be n * p here But I calculated the total m/p which is m/m * q It will happen and I have to divide the total What was the total quantity from the quantities? And m + n so this is my average from here Take out my average and this one is yours It will become average, okay, just check it once.

40:18 p is with m and q is with me, don't make any mistake Just like I did, this one will be yours. Correct Is? Yes, look. The Meaning of Three Numbers a / 3, b And this is the same as the meaning of the number three This much. So it means he is telling you a / 3, okay Mean and average are the same. b + c is Pisces: This will happen. This is equal to you. b / 3 c / 3 + x is equal to its mean. So It didn't make any sense. I wrote it like that Gave. What do I do now? I am from three I will multiply them all. Then a + 3b + 3c = b + c + 3x and I asked you what is it? 3x The value of has been asked. So I'm going to leave it here Give. I will send everyone else here. Then a + 2b + 2c mine will come. Correct answer. Ok? Now look. Look, the

41:05 The average monthly income of the father and mother is This much. The Average Monthly Income of Mother and Her The sun is so beautiful. The Average Monthly Income of Father And his son is so much. Find the Monthly Income of The Father. So what should we do? We need average it is given, we will proceed on the total assumption that whatever The income of father and mother is total income Because the average here was 5000. here If there are two people, then both of them should have Rs 10,000 Will go. Ok? mother and father's meeting The income is average, not that of the mother and father The total income will be Rs 10,000. This way The income of mother and son is Rs 12,000 Will go. Because 6,000 is the average, right? If there are people then the total will be 12,000. Just like that What belongs to father and son will become Rs 20,000. So if you add all these then here you will see two mother

41:51 Father Son will come. to mother father son will come Here. Because it all happens once It is being repeated, right? and you can see it here If we take 20 30 42 then it will come to 42,000. So I need to get help from Father Son so come here It will cost Rs 21,000. So this is the mother, father and son's When I add my salary then I will earn this much will go. Tell me whose father If I want to tell then I will minus mother and son If I give salary then my father's share will be in it If I subtract 12 from this then it gets 9000 Whose father's salary is 9000? that it will come next let's see, see the same thing I told you whatever extra I have I will distribute it equally among all, that is my average will go like it is saying here it is P college P is a college with 180 students in it

42:38 The average marks of all is 88. Correct Is? There is Pay Q College here which has 320 There are students and the average marks of all yes he is 72. Find the average marks of Both the colleges of college together. Now both of these You have to tell the average marks by adding How much does it cost for the kids? so what did I tell you told? I told you this in a simple way What will we do? We will do this. that we all We will distribute it equally. to all I I will divide it equally. that's just my job Is. So what did I do? so what did I You did it, right? First of all I talked to everyone Look here, 320 people have 72 It is 72. 180 people have 88. So I what did you do? everyone because it has 72 Is. So, first I gave everyone equal marks of 72-72. I gave it equally. ok tell me one thing. To you So this is what I have to figure out, when I If divided equally, one person will have

43:25 How much is it? This is what happened to all the people, right? How much do you have? that's your average Went. So the first thing I did was I divided it 72 each among everyone. I to all 72 72 72 72 I distributed it to everyone. Now What did I do? Now you see here that I told them also that it is 72. 180 people who are I have divided them also among themselves in the amount of 72 each. So now How much extra do they have left? Their We have extra 16 left. Every man has There are 16 children. Each man has 16 extras It's saved. And if the total is 180 then that much The extras were saved. Ok? now you see I kept this much for myself and took the rest I divided it 72 each among everyone. That's it. I distributed it 72-72 among everyone. this extra Who survived. Brother, I tell this to everyone I will share it. It has to be distributed equally among everyone, right? So this extra thing that is left over I will use it I will distribute it equally to everyone. so how much is all

44:11 Is everyone there? There are 320, 400 and 500 people here. So I divided the 500 equally. Now from here you can solve it yourself Too. so from here if I do this it's your 180 108 28 / 50 So cut it before five. 5 * 5 * 5 = 25 38 7 6 so it will come to 5.76. So you It looks like if 76 has come then do it Let's take it like that. well your view from here 76 is in one so this 76 of yours is Will go. You can see it anyway. 76 add tax Give it and you will get it. So what did I do? I divided it equally among all of them. That is it Brother. Come forward next. See

44:58 Well, we can do this from basic also. But I will tell you about the deviation here also I will tell you how we will do the deviation. See There are seven papers carrying 100 marks each Everyone's. There are three papers of Mathematics, two One is in English and two are in Hindi. Now D He is getting 45 marks in Maths. The average is if we add all three then it is 45 45 I am getting it. and he is getting it in hindi sorry in english is getting in english 55 55 and getting 60-60 in it. Me I want to tell you, tell me the average. So I've given you What did you say? I divide it equally among all Give. Well you can do it in a very easy way You can do it. 45 * 3 + 55 * 2 + 60 * 2 / 7 Because there are seven papers. So you are seeing 135 + 110 + 120 so 120 110 how much is yours

45:43 Will you go? When you add 135 to 230 and 230 If you give then you will divide 230 by 330 by 365 by 365 Seven is your 5 2 point something will come. So this is your The correct answer will come. You can do it like this also. There is no problem at all. here i am I am telling you the deviation. sorry one I am telling you the deviation. So just because you I am telling you this method again. So What did I do? I first of all 45 45 times see that 45 is the lowest. by the way you You can also assume 45 or any such value. Can you make something that is a little cleaner? As If 79 80 81 82 then I will accept 80 I will take it because 80 is very clean There is value. Understand? This way. So I told everyone what I divided it 45 each among them. from here to there So I divided it 45-45 among seven people

46:28 I divided it 45 each among everyone. Now which Any extra left over, I will distribute it to everyone I will give you equal amounts. so how much extra left? So here they have 10-10 extra Is escaping. There are two people here so 20 The extra is saved. Plus they have 15 each Extra is being saved. how many people here Are? There are two people. That means 30 extra savings Has gone. Total 50 extras left. Seven I will distribute 50 among people. The extras that remain That total amount has to be distributed among the people. So I divided it among seven people. So you are like this You can do it too. 45 + 50 / 7 which is your 7.1 Something will come. So yours is showing 52.1 Something you will go to. The same answer will still come. Ok? Let's see the next question. These You will ask questions to yourself. You will get an average of You have to tell the prime number. There is no trick in this It won't feel like it. You can get it simply between 32 and 69. I want to see the average number. How many will there be? Wool Sum of all and divide by as many numbers as

47:14 Will be. So ask this question to yourself. Yes, okay. Now let us look at this question. So 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. So, I have to tell you their average. So I am simple, I don't have to do anything. I basically what should I do? Well, you are like that too You can do it. Yes, do it like this in it. that the 1:2 ratio given here, I will accept that One man here and two men here. So If one man is here then it will become 12. here If there are two men of 24 years of age then your total weight is It will become 48. If I divide it by three then If I divide 60 by three then my income will be If it goes to 20 then my correct answer is 20. There is nothing to think about in this. Yes, okay? The Average of the Square Off The first five even natural numbers are then

48:01 First five even natural numbers. if only For example, if it were a square, we would make a series of it. You could have applied the formula also. but it is an even number So let's start with the basics. let's see How much does it cost? two is four because first Do you want to tell me, two becomes four? 16 36 64 100 so you are seeing this 100 This is 200 and this is 220 220 and five so 44. Ok? It was done so easily. In this You don't have to think too much. Look at the Average age of the class of six girls. Six There are girls whose average age is x. Meaning you should understand carefully that everyone who The average age is like this x x x x x x. Every x is like this. Ok? Now it is saying Four new girls have ages of x - 2 x + 4

48:47 x so much joins the class. what is the New Average Age of the Girl. what did i Did? First I will distribute x x x x to everyone Give. Everyone got x x. Now the extras What will I do if he survives? That's all I I will distribute it. This is what I do. I have to find the average of everyone. So I all If I distribute it equally, I will give it to everyone First, give x. Gave everyone x. Now let's see Yes, how much extra do we have left? So Here it is -2. It reduced here. -2 + 4 means +2 will be saved. I will take it overall, So +2 will be saved as extra. +8 means +10 The extra was saved. + 10 means +20 The extras were saved. I mean this one which is 20 I will distribute it equally among everyone. How many Are you girls? There were six here. Four more joins I mean out of 10 girls I will take 20 I will divide it equally. So you are seeing Here x + 2 will be my average weight.

49:33 Ok? This question is too much Easy, right? You do it just like this. This Have to start from the basics only. more brain in it Do not apply it. 2300 monthly salary which is Earning for 4 months. 2300 then ₹1800 he earning for next 8 months. again 12400 sorry No. So it's been about 8-12 months here. And he is saving so much money, save it. Used to be. Ok? so he spent that much what is that much? are you earning? Spend He spent this much in the first 4 months. This much He spent the next 8 months and earned this much He has been saving money throughout the year. so this is He got his salary. So this is the total salary He is done. How much did he earn in 1 year That's all I earned. then divide by 12 If you pay, you will get monthly salary here will go. So this is what you need to do. This is by yourself do it. Ok? so what did I tell you told? divide it equally among us all

50:20 Is. This is what we need to do and more It is not there. Look, they all had 20 marks. The pass was 32 32 32 32. everybody has 32 32 I I gave it because he is average. Now I have what did you do? I have given two numbers out of this if two Numbers are so and so than what is The Average of the Remaining Numbers? Ok? Ok? Now look what he is saying. Understand it carefully, very carefully. I I am explaining this to you like a toffee. Is No? So everyone has 3232 toffees. all the which There are 20 people here and each one has 3232 toffees Is. But what did I do? two guys in this are coming out. those who have one One came out with 29 toffees and the other with 31 toffees Has come out. Look, everyone has 32 toffees each Was. But he came out with 29 toffees. One Came out with 31 toffees. So, it bought some toffees I left mine there. Suppose here he

51:06 I kept some toffees somewhere on the side. So You see, he has kept three toffees on the side. And He kept one of your toffees on the side. Meaning These two people should leave, leaving behind these four toffees. have been. You understood this much, right? Everyone had 3232 toffees. these two guys came out Went. These four toffees are somewhere on the side of the table He kept four toffees here and went away. Now I am asking you about those who survived What will the average be? So you got these four toffees These have to be distributed among the remaining people. How many? Are there people left? you know there were 20 people two When people left, 18 people were left. means this I distributed four toffees among 18 people Give. Ok? so I had 32 toffees and I will share this so you can see this Something will come in your point itself, meaning 32 something will come so you should accept it as yours This will come to 32 something, okay so put it like this

51:54 let's do it I hope you understand It must have been very simple in the language of lemon I am explaining it in very simple way I am telling you in a way that is practical what is the average weight of 49 students in a class there are 39 look there are 49 kids each Average age I average weight I 39 39 I gave it to everyone. seven of them whose average weight is 40 kg leaves the class. look now see what He is saying. Now there are seven children who Which weighs 40 kilos. There are seven children who He is coming out of the class weighing 40 kilos. So You see here each weight is extra I am taking it and leaving. Because everybody was 39. Now these 40 ones are coming out so each one is waiting They are taking this with them. means go to minus have been. So here there are these seven people, so these He will go away after minus seven weights. I am understanding yes? because the seven who are coming out

52:40 Weight 40-40 means each weight is extra They are taking it away. So now those who are left in it Seven weights have come out from it. Did you understand it? Correct Is? Now seven more children are coming. whose The average weight is 54. So you know all of The average weight was 39. If theirs is 54 then theirs How much is extra? What did I do? You Think like this. Think carefully and carefully. of all those who are new and those who are leaving I have considered the average weight of everyone to be 39. Start to the end, all the people who are being talked about Here I have considered everyone to be 39. here He has taken 40 rupees and left. That means they too are 39 Was. But he took seven extras with him

…