CAT Coaching – Shortcuts for Arithmetic Problems – Part 1
Look at arithmetic that’s much easier, because this is arithmetic AB=C, or A/B=C. how will you read AB =C? I am using the same logic. This is given in variables. This is given in variables. So, this AB=C, so first, let me first, in math we can write it as A inversely proportional to B, Math or physics? I will say one or the same, A inversely proportion to B when C is constant. When it comes to solving questions, A inversely proportion to B when C is constant in common language how do we take it, more of A is less of B. that’s what, where you need to learn more of A is less of B. so anything like that we will relate AB = C. More of A if it’s less of B, so now the topics which I was mentioning, so speed, distance and time is not a chapter. Have you started your preparation with speed, distance and time? You should not. Because there is nothing to learn. You already know it, that more the speed less is time taken. You are not learning it from a book anyway. More the speed is less time taken, i.e. why AB =C. now what about next chapter, will we time and work. More the efficiency is, less the time. We are employing a better worker; he will finish the work faster. More people they will finish the work faster. These are all different chapters, question types. Now, more people, time and work, pipes and systems, they are all these topics are finally AB=C. Arithmetic this is what we learn. Now why we do we call it arithmetic. Because finally the topics are you might write these in words, Speed x Time = Distance. If you don’t know this, you need to still learn, otherwise you don’t need to. So this is the reason, more of A is less of B. now it can be from the, so there is no point in learning, let’s say, I will show you how to learn this in numbers, because that’s what we need, why do we need numbers? Because most of the questions will be like this. Right? Questions will be in words. Answers will be in numbers. In speed distance time in all, almost all questions will be, questions will be given like a like a story, so it will be given in words. Or a scenario, not necessary it is given as a story; it can be just 2-3 line questions also. But this is the category. Words to numbers. That’s why there is only one thing remaining, learn what is AB = C in numbers. And that’s not at all our level. That cannot be at our level. Because I am writing AB = C in numbers. There is nothing new here. Just that we never thought about these things. 4 x 6 = 24. 4 into 6 is 24, let’s try to find out the number pattern. If I am not changing 24, i.e. if I am keeping the right hand side as a constant, just like as you do in most of the questions, one parameter you keep as a constant. So and if I look at the change here, 4 if I convert into 6, 6 will become 4, nothing is at our level right, what are you learning, you are not learning anything, because the change here is that, what is the change? 4 becoming 6, there is a increase of 2 on top of 4, which is resulting in 6 becoming 4, there is a change of 2 on top of 6. 6 is becoming 4, so there is change, decrease of 2 from 6, so this is the pattern which we need to take out. Note this pattern. Now I can simplify to ½, and 1/3. ½, 1/3 i.e. AB = C. so if it is, 1/3 will be, 1/3 increase will be ¼ decrease. So AB = C, and numbers also know. Variables is A inversely proportional to B, where C is constant, numbers is this ½ increase will result in speed, ½ increase in speed will result in 1/3 decrease in time. And 1/3 is ¼. ¼ is 1/5, that’s the pattern. May be, if you want to generalize this you can replace it by x, so 1/x increase will result in 1/1+x decrease, provided the two are inversely proportional. What is the meaning of inversely proportionality, more of A is less of B. now I am just writing the same AB = C. let’s look at the scenario. So I will make it look like a story, so a person is going from home to office, if he is going at 4Km/h he is 10 minutes late, if he is going at 6Km/h he is 20 minutes early. So find the distance from home to office. So in this case, what is the change here? Change here is speed is ½, 4 becoming 6 what is the increase here? ½, ½ increase will result in we know that right that is AB =C. now how do you know that, you know that it is AB =C. you not always ask the question, as and when you read it, not when you are preparing and all. When you read the question see how the parameters are related. If they are not related, then it’s an invalid question. But if they are related you should always ask the question. How they are related? Are they inversely proportional or directly proportional? Inversely proportional is AB = C. Directly proportional is A/B = C. speed, distance and time are just an example, it’s not a chapter. It’s a chapter for an 8th std guy, not for you, for him also it should not be like that, these are not topics at our level. Arithmetic is anyway, arithmetic I call it 8th std, algebra is maybe up to 10th std. and modern math’s is 11th std. but you can any way bring the level down. As I already told you. So how you solve it. ½ increase will result in 1/3 decrease, this is the pattern. This is the same question written in numbers, because it’s a specific example over here. It’s not a general case. Everything fixed over here. He is going at 4 – 10 he is going at 6, 20 minutes early. And that’s why you will get a specific answer. That’s why you will get a specific answer, that is why answer will be in a number, and not a variable, variable will be when it’s a general case. So now what will be the answer, 1/3 increase, logic here is by increasing the speed here by ½ he will be able to save 1/3 of the original time. And how much time he is saving that’s a given data for the question. How much time he is saving from being, 10 minutes late to being 20 minutes early, 30, so 1/3rd of the original time is 30 so original times is 90 minutes. 90 minutes is 1 and ½ hours. What is the first original speed you considered on top of this only you considered the change? So you assume this is the original speed. So 4 x 1.5, what is the original speed, this is the speed and original time is 1 and ½ so distance is 6 (4 x 1.5 = 6), so that’s the answer. So what is important here is, this is just, how to classify topics. Expecting questions? Since these are all, why it will be easy in a, see these are topics you can relate to. Right? You relate to speed, you relate to time. You relate to percentages, you relate to work. To averages. So because of that what will happen and this is how you should try doing. Expecting questions and it is very very interesting. This is again, you will, make you think. I will tell you now you should not learn speed, distance time as you can solve questions if you want to get the confidence, maybe 4-5 after that you will stop, because you will getting everywhere answers. Speed distance time itself, there is not point, what is done normally because these are all; all play areas where others will make you waste a lot of time preparing for it. They are planning for it; this is considered very important speed, distance and time. I don’t know why I don’t know. It’s not a topic anyway, speed distance time not a topic for you. So here this it will be classification. At least 8 to 10 hrs is spent you teaching this, I don’t know what they teach and I don’t know what you learn. But the fact is it will be divided further like questions on boats and streams, questions on trains, another sub chapter, another subtopic.boats and streams, trains, escalator they are all different right? Trains move like this you need to learn differently and escalators move like this, you need to learn separately, or what’s?