 Hello and welcome to the session. In this session we will discuss a question which says that the middle screen is planning a family movie night where popcorns will be served. There is a constant relationship between the number of people N and P, the number of cups of popcorn which is shown in the table below. Find how many people can be served with 692 cups of popcorn. And here the table is given to us in which the number of people are given as 40, 70, 120 and because the number of cups of popcorn served are given as 116, 280 and 480 and we have to find that how many people can be served with 692 cups of popcorn. Now before starting the solution of this question you should know a result. Now by constant love proportionality we mean that the ratio between two quantities are always same. Now consider and y two quantities y upon x is equal to k where k is a constant then k is called proportionality and this relationship can also written as y is equal to kx which means y is directly proportional to x. Now this result will work out as a key idea for solving what the given question. And now we will start with the solution of the given question. This question N is the number of people and P is the number of cups of popcorn. So given is the number of people and P the number of popcorn. Now we will consider this table in which the different values of N and the corresponding values of P are given to us. Now from the table the ratio to N or you can write it upon N is given as 40 and P is given as 160, 160 upon 40 Now 40 into 4 is 160 so this is equal to 4. Now next 70 and the corresponding value of P is 2 upon 70 which is equal to the next value of N is 120 and the corresponding value of P is 480. So the next ratio will be 480 upon 120 which is equal to 4. Now there is a constant relationship between the number of people N which is the number of cups of popcorn. Now here you can see that the ratio between which is 692 upon N will be again equal to Now from the key idea we know that if X and Y are two quantities and if Y upon X is equal to K then we can write this relationship as Y is equal to KX where K is the constant of proportionality. Now here is the number of cups of popcorn is the number of people proportionality. So we can write this relationship as 24 into N. Now 4 into 173 is equal to 69173. So 173 people are given question and that's all for this session hope you all have enjoyed this session.