Hello everyone, let’s start with the next session of ratio and proportion, which is Direct and Inverse Variation. The first one is Direct Variation. In direct variation what happens. If I consider X and Y are two parameters, Y increases then X also increases. If Y decreases then X also decreases. This form of relationship is called Direct Relationship. That is in direct variation, one quantity increases, the other also increases proportionately and vice versa. So, I can write it as Y is directly proportional to X. In mathematical form, I can say Y upon X is constant. Let us consider an example of speed, distance and time. You know that Speed is equal to Distance upon Time. If Speed is constant so can I say Distance upon Time is also constant? Yes, so, I can say Distant is directly proportional to Time. Now, let us consider. A constant speed of 50 kms per hour, in order to cover 50 kms distance, I can say the time taken will be 1 hour. If I cover 100 kms distance, then the time taken will be 2 hours. That is if distance is multiplied by 2, then time will also be multiplied 2. If the distance is multiplied by 4, that is to cover 200 kms distance the time taken will be 1 into 4 that is 4 hours and so on. That is, the conclusion is, if distance increases time also increases and this form of relationship is direct relationship. In graphical form I can consider the graph of distance verses time as it is a graph passing through origin describing distance increases time increases. Distance decreases time decreases. Now, in the question, two cases will be given to you, describing the relation as direct, and then I can relate those two cases as Y1 upon X1 is equal to Y2 upon X2. Out of these 4 parameters, 3 parameters will be given in the question and you need to find the 4th parameter. By using this relationship I can find the 4th parameter. The practical example if I consider, if you go to shop and if you buy a shirt which is costing Rs. 1200. Now, if you want to buy 5 shirts you need to pay 6000. Yes, cost of 1 shirt is 1200 rupees, cost of 5 shirts will be 6000. So, the conclusion is as the quantity increases the amount to be paid also increases. So, I can say quantity and amount are in direct relation. That’s about direct variation. Next is inverse variation.