He reaches the office 20 minutes late. Travelling at 4 km per hour he reaches 20 minutes late. If he travelling at 6 km per hour he will be 10 minutes early. Fin the distance from home to office. Find the distance from home to office. That’s the question. These kind of questions whenever based on two parameters which are inversely proportional as in this case and that’s very important. Speed and time they are inversely proportional. Here two conditions are given for speed and time or two cases are given. Then there is a direct method using I will call it a percentage equivalent method. Using percentage equivalence e method we can solve not just speed and time there something that you can replicate acrostopic arithmetic or achrosticpics whenever the parameters are inversely proportional. How will you do that. Listen carefully. Find out- we will solve it terms of percentages, very easy to learn and without writing you can mark the answer. This is a very basic question. Below cart level but something you can apply to very difficult questions. There is a 50 pc increase in speed 4 to 6 what do you do is assume anyone as your original case. I will take this one as the original case. 4 km per hour I will take it as the original case. Then fin the percentage increase in speed. 4 to 6 percentage increase is 50 percent. 50 percent or 1/2. If there is a 1/2. increase in speed it will always result in 1/3 decrease in time. 1/2. increase in speed will always result in 1/3 decrease in time. That is the rule. ½ increase in speed will always result in one by three decrease in time. Not just speed and time. That’s the important thing. This is speed and this is time. This is applicable to any two parameters which is inversely proportional. If you know the 1/3 of the original time. According to this rule, the time saved is the given data. What is the time saved? Here its 20 minutes late here its 10 minutes early. So the time difference between two cases is not 10 but 30. That time difference is 1/3T. 1/3T. is 30 minutes. That means t is equal to 90 minutes or one and half hours. We have the original speed. This is what we have assumed as the original speed. We got the time also. Corresponding time is 1.5 hours. So 4×1.5 we will get 6 kms. So this is something which you must note it down. And you can replicate it achrostopic. Speed distance time time and work percentage questions there are lot of questions where you can apply this method. This is an unconventional way of solving – something very easy to understand and easy to use. So first you can note down the solution for this and then you can write the generalized form. I am assuming this four as the original case there is 50 pc increase in speed which is 1/2. 1/2 is always result in 1/3e. If it is 1/2 increase it will result in 1/4 decrease. 1/4 will result in 1/5. Or in other words 1/x increase will result in 1/x+1 decrease in the other parameters if the two are inversely proportional. If you get this the answer is easy, because he is increasing the speed by two kms he will be able to save one third of the original time. Time saved is the given data time saved is the time difference between two cases. 30 minutes. So that’s one third of the original time. From that you will get the original as one and half hours. Original speed we are assuming it as 4. So the distance will be six. So that’s is the technique we will use it a lot of time. To get whenever you are solving questions using inverse proportions. Now how will you write that? 1/x… If A is inversely proportional to b will be a constant AB will be a constant. So any question where AXB is a constant we can apply this AXB is a constant 1/X increase in A will result in 1/X+1 decrease in the other parameter if the two are inversely proportional. So that if you want the constant to remain the same. So that the constant will remain the same. 1/X increase in one parameter will result in 1/X+1 decrease in the other parameter. If the two parameters, that’s important, if the two parameters are inversely proportional. This is something you can use as a useful shortcut in arithmeticS. Something which all of us know is this is inverse proportionality but normally we don’t use this in questions. Start using it to save time in arithmetic. So I will give you a few more examples it’s like you something like XY equal to a constant then you can apply it in speed distance because speed and time is, if the distance is a constant. if the distance is a constant then ST is a constant. If area length and breadth that’s a constant if area is a constant then also we can apply this. In time and work also you can apply this. Because time and work whatever parameters which are inversely proportional efficiency and time taken. Time and work efficiency and time taken. They are inversely proportional. So all these topics you can use this. I will show you wherever you can take XY is equal to a constant then you can apply this method. Lets a very very easy question. If I give you a question like this, price of sugar let’s assume the question like this price of sugar is going up by 20 pc, Price x consumption or quantity is expenditure. If price of sugar is going up by 20 pc, what is the percentage reduction in consumption a family should adopt to get the expenses remain the constant. So the moment you get the constant, if you want the expense remain a constant, once you see this 20 percent you can see this one by five, you can take this one by six as the answer. 20 pc increase in price and the expenditure is constant will result in 1/5 increase in result in 1/5 increase will result in one by six decrease. 16.66 is the answer. These are direct answers. 25 pc increase in price which is 1/4 will result in 20 pc decrease in consumption which is one by five. So one by x will result in one by x plus one. You can apply it in one more question like length x breadth is area. In a question If you want the area to remain a constant you will get constants like this. if area is a constant if length increase by a 33 pc breadth should decrease by 25 pc. 1/3 and ¼ this is solved. Covert it into fraction so you can take 1/x increase will result in 1/x+1 decrease. So these are a just a few basic types of questions you can apply that you will see more questions based on this shortcut as well as the previous ones.