 Don't do guesswork, no point doing guesswork. Take your time, solve, because as I told you, questions will be a little tricky at times, okay? Chalo, let's start, and if something goes wrong, don't worry, now we can delete that question or change that question also at the back end, so no problem, right? So do not panic, focus on answers. I have question solving, not on anything else. No unnecessary gossip in the chat. If you are in trouble, you have to talk to me, that's it, okay? Otherwise, reference from any such messages in the chat box, because I would be having an eye on those who are not able to solve it, okay? So here we go, first question of the evening, start. Full attention, please. So you must be thinking why there is a three third variable in this? So questions will be of such nature that will stretch, which will try to make you stretch your imagination. No questions will be there, which would require something, some knowledge you have not learned, so hence, yes, right? Last 10 seconds, guys, it was very simple question. You don't need a pen and paper to solve such kind of questions also. So in case this question arises, comes 15 seconds maximum, okay? See lots of people have not done it correctly, only 14. That means how many of you could not get this or didn't understand at all, okay? And it was so simple that you will, you know, once I discuss the solution, you will be like, why? Just add both these equations. You will get four x, four x plus four y plus four z is equal to 43 plus 21, right? So hence, it is four times x plus y plus z is 64, right? So x plus y plus z is 16. So did we require anything which we are careful, you know, be careful, yep. So first of all, yep, so as I told you, such questions will be there typically in NTSC. You have to just see and see the pattern and, you know, so those who have not practiced enough in terms of elimination of, so you're not able to see through things. So if you see adding and subtracting equations, in linear equation is a very typical method, typical, you know, tool. So adding and subtracting equation, there will be equations where it needs to be subtracted, right? So did we even go to solution of a linear equation? No, so hence, okay? So let me see only 14. That means everybody is thinking mechanically, that is for sure. You are looking for solutions within whatever you have learned and not ready to go beyond, okay? So here is the first leaderboard. So I think it would be closed. Okay, yes, it is good, nice. So we have, wait, where's the name? Where did the name go? Why is the name not there? Is there some issue there? Why is the name not there? Okay, nevermind, we'll see the next, wait a minute, let me go back and then do again, maybe now it should come. No, the names are not there. Something is light, wait, will that help? Let me see, yeah. So maybe because of that, yeah, someone rightly pointed out, but why should, anyway, so let's just be like that. Okay, now, so let's go to the next question. Okay, nevermind, let it be. For today's quiz, it will be like that. Next time, we'll change. Okay, next question, less number of people, very little, less number of people have got it. So these questions will tell you how the knowledge has to be applied and not to be just retrieved from some artists, so you'll not see such questions. These all questions are fabricated, we have made it. Just to make sure that you put your mind before solving. Again, you have to do some of the questions, maybe. Similar to previous question, yes. So those who are trying to solve the questions, they are going in the wrong direction. You don't need to solve them. Correct, time's up, and yeah, so we'll see. A lot of people have made a calculation mistake, so I think 22 and 31 would be similar, but most of you have not done the calculations properly. Okay, so here was the question. Right, you needed to first, again, based on summing and finding the difference, yes. Add both the questions, you'll get 7x plus 8x, that is 15x plus 15y is equal to 45, right? So x plus y is 3, right? And if you subtract, second from one, you'll get minus x plus y is equal to five. So x minus y is minus five, correct? And then you have to find out x square minus y square, so you don't need to find x and y, simply x square minus y square is x plus y, x minus y. So that is three times minus five. So minus 15. Understood, everyone? So what is the catch, what is the learning? Don't need to solve every time. So don't really have that mechanical method of, okay, first two equations are there, let me find x and y. Always have an eye on what is the demand of the question. What happened? You got automatically went to this, okay, let's go to the leaderboard. Okay, very good. Okay, so good, let's go to the next question. It will take some time, so don't really try to guess what's here, time and solve. So this question is based on finding a linear equation. Okay, in the next academic year, you will have to deal with coordinate geometry where again, linear equations will be a vital component and again, these kind of understanding would be required. So don't rush through, take time and solve. So now, eight, seven, six, five, four, three, two, and one, let me see the performance. How many of you have, oh, that's nice, good. So most of you have got it correct, but then lots of you have not got it correct. How many of you? Yes, you have to read, that's the agenda. Okay, so where did the, oh, went away actually, okay. Just a minute. Yeah, so this was the question. Okay, it was fairly simple question, you just needed to frame it properly. So you are walking on the lines as that twice the sum of your coordinates. So let's say your coordinates are X and Y, is three more than thrice the difference of the coordinates. So, you know, sum of your coordinates, that is twice of your coordinate. In one line, you can write an equation. It's three more than, so three plus thrice the difference. So how quickly you can frame the equation was the, yes. So hence it is two X plus two Y is equal to three plus three X minus three Y, which will lead to, if you solve it, you'll get X minus five Y plus three is equal to zero. Yep, so hence, Surya, so that's what many people do. So, you know, all these, and there are words in mathematical questions, our mindset is like that only. So we get confused, we tend to miss values because now twice is the information. Purposefully written like that, sum is an information. Only one numeral is there, which is three. Otherwise, again, there is thrice, okay. And there is difference, there is, you know. So this is something where someone was saying mind-body coordination, what was that? I-I-N or that I-hand coordination. You have to, here, where is your I-hand coordination here? Okay, so you have to improve that here now, okay. So let's go to the next question. Where was it? Here. Okay, so let's see the leaderboard. Ah, hand-eye coordination. So here, the hand-eye coordination should be here in solving problems, not killing some arbitrary virtual enemy. Okay, very good. So next is this. Show your hand-eye coordination here. Next question. Some of the numbers are 64 and their difference is 32, which of the following is not a factor of the difference of the squares of the two numbers. Again, lots of words. Lots of words, not our direct linear equation type. Yes, they are not. And henceforth, there will not be direct questions. There is no obvious answer here. There is past three seconds. Very well done. Let's see how many of you have got it, correct? Okay, nice. Most of you have got it, correct? Ah, now we understood, Aryan, this is the plight of so many people. It takes a long time to understand the, right? You know, just like your video game level one, where you need to figure out what's happening, right? This was the question. So some of two numbers is 64, very easy. Again, similar type. You don't need to solve. So linear equations are not always meant to solve for x and y. So you didn't need to, you know? So the question was, which of the following is not a factor of the difference of the squares? So x square minus y square was to be found out. So x square minus y square is x minus y x plus y, which is 64 into 22, and then problem was mathematically easy, right? So which one is not a factor? Clearly, 44 is a factor. 11 is a factor. 88 is a factor of this, correct? But 33 is not because there is no three here, right? So hence D was the correct option, correct? So you would be expecting, you would be thinking, how come I'm not getting the, you know, questions to find out k, and questions to solve a pair of linear equation and typical questions like that. So you will not get all of that. So you have to widen your horizons now. Okay. So those questions in exams and assignments, okay? Okay, next, let's go to leaderboard. Good one. Let's go to the next question. Okay, ready guys? Now this is typical. Is it typed wrong? Yes, Mezad. Where is error? Where is the error? Fifth grade question. So Mezad has already solved it. Very good. Let's see. Okay, most of you are worried. So there are still 20, 22 people didn't get it. Okay, very good. So most of you, you know, one way is to look at the options and solve it and that itself will solve the question. So if you see, if the digit in the unit place is three more than the digit in the 10th place, okay? So the only option is B. So lots of people would have solved this question. And right now, so the unit place is three more than the digit in the 10th place. So the only option possible was B and you could have solved this. But just in case you wanted to solve it, the, you know, it would be like this. Let's say X and Y are the digits. So the digit or the number is 10X plus Y, okay? And the ratio to the sum, they are saying X plus Y, right? So 10X plus Y is the number. And X plus Y is the, what? The sum of the digits. And it is given as four as two one. So just in case you wanted to solve this formally, so it will be 10X plus Y is equal to 4X plus 4Y. So that means 6X is equal to 3Y. So 2X is equal to Y, okay? And then you go to the next equation where it says unit place is three more than. So Y is equal to three plus X, right? So these are the two equations. So you can write Y is equal to 2X. 2X is equal to three plus X. So X is equal to three. So hence Y is equal to six. So three and six, 26. All right? So hence in MCQs, yeah, you can take directly whatever. This is a formal way of solving linear equations in two variables. So in case of NTSCs and other exams, it will be better to go this way up. Okay, that's a knack you will develop over a period of time. You go on doing this again and again. So you can eliminate quickly. All these were waste, right? So there will be question, there will be, so you don't need to, you need to solve there. So this is an exam trick, not for general practice. For general practice, please adopt this. Because until you are very sound here, this will always problematic, okay? So general practice, go formal way. When an exam, any way is okay, okay? Sure, let's see. So there is some shuffle, nevermind. Let's go to the next question. Here is the next question. Good, so here is C. So good that most of you, only 50% are able to solve it. The rest 50% are struggling. This was a plain and simple case of solving the linear equations. And that too, very easy ones, right? So, and that too again, you didn't need to solve fully. Half solution could have helped you here also. Okay, no, two x plus three y is equal to five. On the same axis, okay, that means you didn't understand the question. Course of an enemy submarine that's plotted on a set of rectangle axis is this. This is a submarine. On the same axis, the course of the destroyer is indicated by this. The point x, y at which the submarine can be destroyed. So basically what will happen? This is a submarine, it fires something in this direction. Right, and the destroyer, destroyer is here. Right, so this is the line of submarine. This is the line of destroyer. So when will it destroy it? When they meet, okay? So point of intersection was to be found out. And the application, right? So hence, two x plus three y is five. And hence, x minus y is 10. You just simply needed to multiply and made it 20. And then what will happen? Subtract, you will get five y is minus 15. So y is minus three and game over. That's it, you stop here. Don't go for x, y because only one is minus three. Right, but while you do it, you need to be doubly sure that one component which you just found out. Okay, right? So this is what is the solution. So y is minus three. I hope you understood this. If you put it in x, you'll get seven. You put this in this equation. Y is equal to minus three. You'll get two times x plus three times minus three is minus nine is equal to five. So two x is equal to 14. So x is seven, right? No big deal in this question. Why did people struggle in this question? Guys, all understood? Yes, obviously, it will definitely take time, right? So you have to develop both, both, none of, you know, only one mechanism will not help. So you need to learn the exam tricks and also learn the basics. Only one will not help. Both you have to learn. Okay, so Niket is maintaining the lead. Good, Aditi, good, Shreyas. And Shreyas is now on second place. Aryan, Moomita, what happened? INR is like top five here. Pranav, Surya, Abhipsa, Siddharth, Karthik and Eden. So 60% people are from Indanagar. Okay, so this is done. Next question. People do not like serves. Use your ninth grade skills, guys. The question is based on that. So those people who remember those techniques, they won't require much of time to solve this one. If you go for solution, go for solving, the way you have learned in the equation, it will take some time. Okay, but otherwise it's very straightforward. Very straightforward. Yes, conjugates. Now you got it. So, you know, knowledge of conjugates will make you solve this question within no time. See, all these questions have been, you know, designed in such a way that it doesn't take much of time to solve. See, Ananya is asking, sir, parallel means non-intersecting only. Last class, you were not there, Ananya, last. See, only 15 people got it correct. Last class, I talked about how two lines, two parallel, two lines might not be, you know, they might, what is that? They might not be intersecting, yet they will not be parallel. Right, yes, so one line is on the roof, another line is on the floor. They are neither intersecting nor parallel. Okay, only X and Y. Yeah, only X and Y only. Yeah, so don't worry. So where am I saying there is only X and Y and all that? So anyway, that was not the right option, okay? So, in this question, so what? You know, so anyway, that option was not correct. Anish, so hence you can't really get hooked on to something which is, right, which is the most correct answer in this, most correct option, right? Here also represent two non-parallel, non-intersect. Definitely D is not the correct answer. Okay, they do represent something which is others. A was the first answer. Why is that? Because what is the, you know, the rule for coincident lines, right? A1 by A2 is equal to, for coincident line, you have A1 by A2 is equal to, B1 by B2 is equal to C1 by C2. That is the ratio of the reciprocals must be same. And all our half, yes, you have right, we, you know, got it. So, basically it was 2 minus root 3 and the moment you saw it, yep. So, 2 minus root 3 is equal to 1 by 2 plus root 3. That's what I was talking about. If you knew, if you had this knowledge, immediately you would have figured it out. Okay, 2 minus root 3 is always equal to 1 plus 2 plus, 1 by 2 plus root 3. And similarly, 3 minus 2 root 2 is also equal to 1 upon 3 plus 2 root 2. Why? Because 3 minus 2 root 2 is root over 9 minus root over 8, right? So, whenever such kind of thirds are there, okay? So, hence, done. So, hence, what will happen in this case? Basically, they are all same. So, this and this are same. This and this are also same. And you have to just make sure that you don't make a mistake here. This was minus root 8, so you have to take it on the left-hand side and then solve. Okay, so all the ratios are 1 by 2. So, first option only was correct. I hope this is understood by all. Any trouble in this question? It was simple a1 by a2 is equal to b1 by b2 is equal to c1 by c2. Yes, and it was better. Yes, understood now. So, you will not lose marks because you would not be knowing the question or the solution. You will lose mark because you didn't pay enough attention to the question. Between a and d, okay. Two non-parallel, non-intersecting lines are when they are in 3D space. So, imagine a line on the roof. And imagine a line on the floor. So, floor and roof, two lines are there. They are non-parallel. Neither they are intersecting. Okay? Coincident lines don't intersect. Sir, coincident lines don't intersect. No, so we have intersection is one point. Intersection is one point where, you know, one point common is called intersection. Coincidence is one point. All points coincident is called coincident. Okay, so, you know, common is understood anish. So, intersection is only one point common between two lines. Coincidence means all points are common between the two lines. Do you get the difference? Sorry, so let's go to the next question. Sir, so don't can be right. D can't be right. How? Again, why is D right? Do these line represent a non-parallel line? Do they represent a non-parallel line? Do they represent a non-parallel line? Answer this question. Anish, do they represent non-parallel line? They don't represent non-parallel line. They are parallel lines, right? See, two coincident line anyways will be parallel to each other. So, they don't represent non-parallel line, right? And they are non-intersecting lines as well. Intersection, as I told you, yes. So, intersection is when only one point is common, right? Coincident is when all the points are common. So, do these lines represent a pair of line where only one point is common? Okay, is that okay? Again, infinite points common is coincidence. Only one point common is intersection. So, they intersect only at one point, okay? Let's go to the next question. So, not much of a, okay. So, now people have, Arayan, what happened to you? Umita? So, in such questions also, when you have a very clear-cut option there, please go for that. Don't really, you know, if let's say there is ambiguity in the question also. When you know one in this problem also, no one could deny this. Can anyone deny this that this is wrong? This one, in such case, please mark that which is absolutely correct. Okay, next question. Be careful with this question. Not straight forward. We are bounded by the y-axis and the lines. We are bounded by the y-axis and the line-axis. I mean, how many lines are there? My case is one. Three x minus four is the solution. Be careful with this. Be careful with this. This question requires some attention. And previous knowledge. So, if you don't have previous knowledge, nine grade knowledge that is, then it will be difficult. Options could be very close. Let me see the result. I'm interested in knowing the result of this one. Hmm, most of you got it wrong. Why, by, why? Lots of people have written 31. All, why, anyone who can tell me how is 31, sorry, not 31. How is B the correct answer? Why did you go for the parallelogram? Lots of people are now here struggling. Now, these are the application of linear equation, guys. So, please pay attention to this. Yeah, they hope. What were the questions? Questions were three x plus four y. Three x plus four y is equal to what? 12. And three x minus four y, right? Yes. So, x minus four y is equal to 12. Immediately, you have to find out the point of intersection with the coordinate axis. That's it. And the game was over. Put x equals to zero here. You'll get y is equal to three. So, zero comma three is one point on the first line. Okay? Put y is equal to zero. You'll get x equals to four. So, four comma zero. Immediately, you have to be very fast with this. Yep. Yes, it's better. Just quickly draw a rough diagram. So, this is the first line. Second line, put x equals to zero here. You'll get y is equal to minus three. So, this is the point. By this time, you would have guessed that what is the triangle we are talking about. And then, put y is equal to zero, x is four. So, again, this point. So, hence, this is the line. So, which area I'm talking about, this area. Okay, how much is this one three? How much is this one three? So, what is the area? Half into three into four. Yes. Sorry, half into six into four, which is 12. 12 is the area. Six, 12. 12. That was the catch. So, half into six into four, right? Six is the base. Six. So, answer is 12. Now, the only possible was this. Why? Because equal to half the area of five by five square. No, it will be 25 by two, which is not 12. Oh, okay, like that. Okay, no problem. So, equal to half the area of the parallelogram with length parallel side as four. So, this is four into three, 12. But then, there is a half here. So, it will become six. So, this is also wrong. And this one, half the area of rhombus. Rhombus area is half into three into four. So, again, it is six. So, all were wrong, only this one. Okay, so, what was the learning in this question? Point of intersection with the axes. How do we find out? Put x equals to zero, y equals to zero, right? Put x equals to zero, you'll get y. Put y equals to zero, you'll get x. Quickly plot the graph quickly, right? Because last year itself, you learned how to plot zero comma four, four comma three and all that. So, if you do that, draw the diagram. It will be a regular geometrical shape. Use your knowledge of finding the area, solve it. That's it. So, hence, those who paid attention to plotting and were focused while solving would have solved it. But, what? See, Ananya, you're saying it's easy, see the report. 31 people got it wrong. I want to know why it was marked like that. Anyways, so only 19 people could get it right. So, here is the leaderboard based on this question. Okay, so, oh, what happened? What happened? What happened? This is something. Anyways, chalo. Now, take deep breaths. Next question, please make, please do not, please do not make a mistake, okay? Let's go to next question. This is typical question, you can solve it. But, you need to be very quick on taking the variables and solving it quickly. And, there will be a trick in this question where I don't know if you adopt that. Let us see why solving, I'll tell you. You will need to solve it, don't hurry. Don't rush through the question. I can see a lot of people just marking it just like that. Don't do that, solve it. So, you're saying there is some third-party who is marking it on its own. So, 28 people have done one on their own. Oh, I see, their machine is not working properly. Anyways, no problem. Aniga, you're back in Bangalore. How are you? You're back in Bangalore. Now, you've got Aditya and I on the final result. These are the small, small things you must, you know? So, you have to eliminate that you don't require. These sessions and practice give you that sense. So, hints, yeah? So, two crucial things were there in this case. Two things. First, you need not use, as in substitution. And second, you eliminate something which you didn't want. Okay? So, lots of people could not get it but most of you have got it. Yeah, so, I hope you understood the question. Go to the question. Yeah, so, what is this? Let's solve it now. So, two men and so, immediately if I have to solve this, I would do this, that I will take, you know, I will not write all those steps here because this is our, you know, 100 second question. So, I will say two men and seven children complete a certain piece of work in four days while four men and four children complete the same work in only three days, right? The number of days required by one man to complete the work is, so I have to find out one man's work. So, let that be M, start from here itself. M, and choose those, you know, variables or symbols which will connect to the, you know, real variables here. So, M for man and C for child, let's say. So, one day's work of M will be one upon M. So, basically he completes the job in M days. So, in one day he will complete one upon M. And they are saying two men. So, two men's work is how much two upon M and seven children work will be seven upon C. This is the work of two men and seven children in one day and it is given that it is one upon four. So, you must be very, very clear on this, okay? So, two upon M plus seven upon C. How many of you got this equation? Yes, right? So, you have done this type of questions, right? And next one was four upon M plus four upon C is equal to one upon three, that's it, right? Now, don't substitute let X be one upon M and all that. Don't do all that, okay? Eliminate, what will you eliminate? C, and done, right? How to eliminate C? Multiply this by four and multiply with this, this with seven and subtract and subtract directly. So, hence, if you see, it will be eight by M. So, C wall apart will be gone and this will be minus 28 by M is equal to one by four minus one by three, right? So, hence, it is minus 20 by M is equal to minus one by 12. Am I right? No, I'm sorry. Yeah, three minus one upon 12. Am I right? Did I do it correctly? Three minus four? Yeah, that's fine. No, something wrong. Did I not do it correctly? Four upon, oh, sorry, sorry, yeah, my mistake. So, this is one. This will be one and seven by three, sorry. So, one by seven by three, my mistake. So, the options were not matching anyways. So, minus 28 by M, let me do it fairly. So, I forgot to, you know, this is one minus seven by three, yep. So, don't do that. So, minus four by three. Now, it is fine, correct? So, that means this is minus five of one. It will become plus into three is equal to M. So, M is 15 directly. If you think you have to eliminate the other one and then find M, your wish. But I would go for only one variable so that I don't need to, because the moment you do that, you add to more number of steps. More number of steps means more mistakes, probability of more mistakes. So, hence, always try to eliminate which you don't want, okay? Right? So, whichever way you are comfortable, there will be cases where, you know, directly finding out what is demand of the question will help you solve it faster. Anyways, so let's go to the lead board and see. So, you know the pattern now. In the work type problem, you have to do what reciprocal equations will be there. Okay, so let's go to the next question. I think most of you will make a mistake in this question. Questions would appear to be easy, but they will always try to, you know, make it a little tough for you. See, one thing they are going to play with is your impatience. It is going to play a very major role in your career. Should have set it in starting. No problem, that's next time. I have been saying this almost in every question. So, this impatience, if you don't work on it, it will become a big trouble, okay? So, answer is, see, oh, oh, oh, oh, oh, oh, oh, oh. Right? It wasn't hard, but then see the performance. 15 out of around 16. That's so sad. Okay, so how many of you did not understand the question? Question understanding was not a problem, I believe, but then you did not read the question properly. Most of you would have done mistake over there. Is it sum of two integers is 88. So, X plus Y is 88. If the greater is divided by the smaller, let the greater one be X. So, divide by smaller quotient is five. So, five Y plus remainder is 10. These are the two equations done, isn't it? So, hence, what will happen? You can just deploy this X here. You will get, and you have to, okay, you have to get both the numbers. So, hence, it is five Y plus 10 plus Y is equal to 88. So, six Y is equal to 78. So, Y is 13. Y is 13. So, most of you would have jumped on this mark, this. But the question was, the greater integer is more than the smaller number Y. So, what was the greater integer then? So, 88 was the total sum. So, X would be simply 75. So, you have to find out X minus Y. The question was, find X minus Y. 62 was the answer, right? So, you did not read that question, maybe properly. And see, most of you have marked it wrong. I want to know, where did you guys go wrong? Anyone of you who have made it wrong, can you explain what happened? Why did you make it wrong? This was so simple question. Is that something which you haven't learned or something like that? Is this something out of the equation forming? Jumping on the answers, okay. You know your issues, issue areas, correct Niasi? I found 75 and marked it by mistake. That's exactly what I was, yeah. X is equal to five Y plus 10, wasn't clear. So, now it is clear, Aditya. Is it now clear? Clear now to everyone? Yes. So, I'm telling you, if at all you are going to suffer in any of the competition, it will be because of your impatience and lack of focus, that's it. Not because of lack of knowledge, okay. Chalo. Okay, so next question. Before that, the leaderboard. Oh, lots of changes are now occurring, okay. Good. Very good. Chalo. Yes. Again, same instruction. Deep breaths, deep breaths before the question. Calm your nerves down, read the question properly, then attack it. Equation in three variables. Three variables, equation, require how many equations? There are three variables. Options also are little deceptive, but yes, if you calculate it properly. The result will show what was easy. Okay, let's check. Okay, okay, okay, okay, okay, okay, okay, okay, okay. Most of you have got it correct. So, thanks. Good. So, you mark D and you get Gupta, why? Why did you mark D? Okay, so very easy question, yes. You have to simply equate it to K. Simply equate it to K. So, you'll get X is equal to 4K. Y is equal to 3K and Z is equal to 2K, correct? Yes, third equation was there, yes, that's right. So, there are three equations already. One, two, and three. Yeah, you can do that. Option, see option one is definitely there, you can always do, you're gonna put these values and it is 62. But if, let's say it is a subjective question, they are asking you, find X, Y and Z, then what will you do? So hence, this is a formal way. So, now you can put, plug this here. So, what will you get? 7 into 4K plus 8 into 3K plus 5 into 2K is equal to 62, right? So, what is it, 28K plus 24K plus 10K is 62. So, what is it? 62K is equal to 62. So, K is equal to one. So, the moment you get, wait, Y is not writing, like a, K, there is some lag. Come on, something happened, wait. Yeah, so K is equal to one, right? So, this is K equal to one. If you put K equal to one, you will get X equals to four, Y is equal to three, and Z is equal to two, isn't it? Right? Yeah, no, there are three equations. I just said that, because I wanted to trap you guys, and you fell for it, correct? So, you know, I reinforced your doubt, and you fell for it. Exactly situation, exact situation will be there in an exam. So, there will be environment, sir, God, DC, yes. That's what, no, so that's what I'm saying. Exactly similar situation will be there, and you will be falling for it, the question setter will be setting a question to trap you. Okay, never mind. So, let's go to the leaderboard, and the final one of the evening. Hmm, cool. So, Aditi comes on second position now. Okay, Nikkei, only one question left. Chalo, anyways, all of you, good show so far. So, let's go to the next, and the final question. Here is the final question of the evening. Let me see how many of you get it correct. I will check the names who have marked it correct. I already marked it, that's so nice. As far as Nikkei's theory, it is some machine marking. If all marriages happened within the village, it is. In a given village, two-third of the men are married, two-thirds of the women. The population of the village is more than 1,000. If all marriages happened within the village, then find the smallest possible population of the village. Assuming there are only adults in the village. Very good question it was. I don't know how many of you have got it correct. Let's see. Only 49 item did, 50 only. So, thanks up for many. But thankfully, most of you have got it correct. Oh, how many of you got it correct? Tell me here. How many of you got it correct? Surya got it correct. Asresha, Sharan, Laksh, Shobita, Laksh, Kiranmai. Okay, very good. Nevermind. And how many of you could not solve it? You need some help. Okay, nevermind. Anyway, I'll solve. So, in a given village, two-third of the men are married. So, let's say in the village, M is the population of men. So, M was population of men and W, R population. Oh, sorry, I'm not showing it to you. So, M and W are the number of men and women in the village. Now, two-third of the men are married too. So, obviously, two-by-three M is going to be equal to three-by-seventh of W marriage, one-on-one function. So, two-by-three M is equal to three-by-seven W, right? Now, you have to find out the minimum possible population of the village. So, I will start with, let it be K. Now, K is an integer. And that is where I will play with. So, K is an integer. So, what is M then? M is equal to three-by-two K. And what is W? W is therefore seven-by-three K. Okay, and what is the population, guys? Population P is M plus W, because only adults were there, there's no children. So, M plus W, that means three-by-two K plus seven-by-three K, correct? This is the population. So, what is the population? Let's solve it. So, K common, it is three-three is a nine plus two-seven is a 14 divided by, this is the, so 23-by-six K, is it? Am I right? Yeah. So, 23-by-six K, this is the population, okay? So, 23-by-six K is greater than thousand. This was given, isn't it? 23-by-six K is greater than thousand. So, K must be greater than thousand into six upon 23, okay? So, and then, that means K has to be a multiple of, or, you know, K is 23 divides K for sure. No, not two K, 23 has to divide K, because K is an integer, right? K is an integer. So, this item should be integer. This is an integer, and that integer, such that it is more than, so what should be the, you know, minimum population so that it becomes a, so the nearest possible multiple of 23, just above thousand is 1012, okay? So, if P was 1012, then I think this is 44, yeah. So, then you will get K as an integer. In all other cases, you will not, okay? So, 1009, if population was 1009, you will not get K as an integer. And we have to play on that, K was an integer. So, 1009 is ruled out, 1012. So, you have to just check which one is the nearest multiple of 23, that's all. So, 1012 is the nearest multiple of 23, just above thousand. The population, you only consider the married people, right? No, total. M is the total number of men available. W is the total number of women available. So, two-third of men is equal to three-seventh of women. But it, is it okay? So, but the population was M plus W. Total population was this. Is that understood? So, here, see, use of linear equation with some kind of number theoretical knowledge as well. So, K was an integer. So, you have to find out a K, which is just above, just above this thousand into six upon 23. So, what should be the nearest possible value of this and got, where I calibrated everything from there on? Okay, no problem. But you understood the method, right? How do we know one man is married to, oh, oh, oh, oh, okay, I didn't. Let's, let's not get into that. So, yeah, that is, okay. So, yeah, okay. So, this is, I hope you learned how to solve these. These are not straightforward question, guys. So, you would have never encountered such questions where you are dealing with some uncertainties. You are not dealt with such questions where we have dealt with uncertainties. And then also, the data given in the question should be, it's sufficient enough for you to reach out onto this conclusion that the minimum possible, this thing is 1,100, 1,012. Is this question understood? The solution understood, guys, solution understood. So, you can expect similar questions in, you know, all the competitive exams will be like that. There will not be any straightforward questions. NTSC to an extent will have few, but then all the other exams that you are going to face later on, they will test your application on, application of knowledge. So, how much do you apply? So, here, not only the linear equation part, you learned something last year, this year also you'll be learning and you know, you know, divisibility tests and all that. So, that is also part of the question. What is the question? Kaman also will have these kind of questions. Let's Kaman tell you that. Okay, so, sort of suspense from my side also, no? Okay, I hope you understood the different types of problems and you know, it will refresh your concepts. Please keep solving more and more problems and one more learning is, try to retain your observations. For example, one observation of conjugate search, you have all forgotten, but then if you retain that, you will save some time. Okay, chalo, see you guys next week. By the way, all of your schools are opening, right? On Monday, anyone whose schools? So, now we will be going back to our, so for CHK people, we will be doing on Saturdays. For all others, we will be doing on what we used to do. Like afternoon, right? So, the classes would be from 3.30 onwards, 3.30 to 4.30 and 4.45 to 5.45, something like that. Okay, yes, online classes only. So, all classes would be online. For all other NPSs, the way we used to do prior to, you know, this lockdown, we will be following that time. So, we'll be starting at 3.30 and two hours from then on with some break and for CHK, it will be full Saturday, guys. And CentreMars will continue as we are doing right now. Yeah, and then NTSC classes will be on Thursdays evening, 7 to 9. Okay, so this is, yeah, so again, same thing. Same, yeah, so next week onwards, classes are resuming from 3.30 PM. Now, we will be doing instead of morning or anything else. Oh, I'm sorry, leaderboard, yeah. Sorry, my bad. Yes, so before that, final leaderboard. So, good that you reminded me. Okay, here is the final leaderboard. And, and, and, and, and. Okay, so this is the final, so I need to keep after messing up with last two questions also. So, your previous karma helped you. Good, well done. Shreyas, well done, Aditi, good. Well done, Aden, Aditya, very good. Aryan, very good. Shobita, keep it up. And Nandini, very good. Pranav, keep it up, Laksh, very good. All of you, and all of you who have participated and got some position, try to improve next time. Good to see new faces in the top 10. Very good, guys. Keep it up. Bye-bye, take care, and good night. So, yes, I was explaining those, you know, the schedule. So, I hope you will get anyways the notification. So, through the WhatsApp. Okay, bye-bye, take care, guys. Good night to you all of you. And, Aditi, are you saying something? Could you go back to time and work queue, right? Time and work question, okay. Which was time and work question? This one, Bolo, tell me, what is the problem? Yeah, Bolo, tell me. Any explanation needed here? Explain the question. Okay, see, two men and seven children complete a certain piece of work in four days. So, we have solved these kind of problems in our, okay. But anyways, chalo, once again. So, two men and seven children are, doesn't mean one third of the men aren't married. Sreejani, just wait, I'll explain Aditi and then to you. So here, two men and seven children. So, let's say a number of days, number of days taken by one man to complete the job, to complete the work. B, M, okay, M. And same for a child, let's say, it is C, is it okay? So in one day, in number of days taken by one man to complete the work, B, M, clear? And for child, it is C. So, one man in one day, how much work will he do? One upon M, is it it? So, M men are required, oh, sorry. In M days, he completes, in M days, he completes one job. So in one day, he will complete one upon M job, right? And similarly, one child will complete one upon C job in one day. How many, they are saying two men were required. So, two into this and seven into this. If these people, so this is what? What is this? This is nothing but one day's job of two men and seven children, one day job. This is one day job of two men and seven children. And together, they are saying they will take four days. So in one day, how much work they will together do? One upon four. This was LHS was one day work of two men and seven children. RHS also is one day work of two men and seven children. So I can equate them, correct? Similarly, four men and four children can do it together in three days. So this is one day job of four men and four children. This is one day job of same four men and four children. Which is three days, right? So they are doing it together. They are taking three days. So one upon three days they will take to do, you know, or one day job is one by three. Is that understood, Arithya? Now to just solve these two equations to God to get M and C. So we solve the equation directly to find M to be equal to 15 days. Clear? Then Srijani, yes Srijani, what was your question? Arithya, clear to you? Srijani, tell me, what was the question dear? So you said, okay, bye, take care. Srijani, what was the question dear? The last one, yes. Your question was, for the last question, doesn't mean one third of the men aren't married. Yes, that's true. Yes, they aren't married, right? So but then there was no questions around it. One third men were not married, that's fine. Okay, now understood. So one third were not married. And two seventh, no, fifth, five seventh of women were also not married. Okay, so men and women, number of men and women were different. But you took it at the whole population, right? No, see, question was this. That two third of men, this is a number of men who were married. Now number of men who were married, yeah, four seventh. No, what was that? Two by, three by seven, right, so correct. So two third of men were married. Now obviously number of men who were married will be equal to number of women who are married. So how many women were married? Three seventh. Okay, whatever was the total population of women, three seventh of this were married and two third of men were married. Okay, and total population P was M plus W. I simply considered this to be K so that I get only one variable to deal with. So M becomes three by two K and W becomes seven by three K. So that means my total population becomes three by two K plus seven by three K. That means 23 upon six K, this is the total. So population is of this form, 23 by six, 23 by six K. Now obviously 23 is a prime number. Okay, so there are two ways of, you know, so the population, population has, is a multiple of 23, you see, this population is a multiple of 23, correct. So what will be that, that number above 1,000, that number just above 1,000, which is a multiple of 23 is one, zero, one, two. So if P is equal to one, zero, one, two, then what happens? I get one, zero, one, two is equal to 23 by six into K and I get our integer value of K because 23 goes 44 times. So K is six into 44, which is an integer and that's what we wanted. If P was anything else, anything else like 1,009, the first option, then what would happen? Then it would become 23 by six into K and then K would come out to be a non-integer into six by 23. Now you divide this, you will get 43 point something into six, which is a non-integer. So hence 1,009, 1,009 is not an option. Why were others not an option? Because they are, they are all multiples of 23, if you see. They're all multiples of 23, but the lowest possible was this. So hence the option 1,01. Clear? Okay, bye. Take care guys. See you. Bye-bye. Stay safe. So, who's this? Aryan. Yeah, Aryan Baloo, tell me. Sir, since we already get the population as 1,012, why do we need to solve for K? No, no, I was just explaining. Explaining, not needed. I was just explaining that CK, if you take something else, K will become non-integer. Hence, you don't need to solve K but you need to be convinced, no. 1,009 is ruled out. That's why I do. Okay, bye guys.