 Hello and welcome to the session. In this session we will discuss the question which says that calculate the index number for 1985 taking 1980 as the base year using weighted average of price relative method from the following table. Now here in the table the weights commodities are given to us as A, B, C and D and their corresponding weights are given as 2, 4, 3 and 6. The price per unit in 1980 for the commodity A is 20. Then for B, C and D it is 30, 40 and 50 respectively and for the price per unit in 1985 for the commodity A, B, C and D is 45, 60, 62 and 75 respectively. Now if the weights are now changed so that weight for A is 3 and weight for B is 2 and the total weight is 15 and the value of index number in 1985 with changed weights is 173. Calculate the weights applied to C and D. Now before starting the solution of this question we should know a result. And that is by the weighted average of price the relative method p1 is equal to summation of p1 over p1 into 100 the whole into w whole upon summation of w which is equal to summation of w into x whole upon summation w where p1 over p0 into 100. Now here p01 is the price index number for the current year with reference to the base year w denotes the weights and p1 over p0 into 100 are the price relatives where p1 denotes the current year prices and p0 denotes the base year prices for the given commodities under consideration. Now this result will work out as a key idea for solving out this question. And now we will start with the solution. Now first of all by using the weighted average of price relative method we have to find the index number for the year 1985 taking 1918 as the base year. Let us draw a table for the given data. So we have drawn the table for the given data and in the first column we have written the various commodities. In the second column we have written the price per unit in 1980 that is per year 1980 is the base year for the year 1985. The price per unit in the year 1980 will be denoted by p0 and for the current year that is the year 1945 the price per unit will be denoted by p1. And in the next column we will find the price relatives for the year 1985 that is we will find x which is equal to p1 over p0 into 100. Then in the next column we have written the weights which are given to us and in the last column we will find w into x. Now for the commodity daily the price relative x will be equal to p1 over p0 into 100 which is equal to 45 over 20 into 100 which is equal to 225. Then for v it will be 60 over 30 into 100 that is 200 and for the commodity c it will be 62 over 40 into 100 which is 155. Then for d the price relative will be 75 over 50 into 100 which is 150. Now it is fine w into x now here 225 into 2 will be equal to 450 then 200 into 4 is 800 and 155 into 3 is 465 and 150 into 6 is 900. Now the sum of all the values of w will give us summation of w which is equal to 15 and the sum of all the values of w into x will give us summation of w into x is equal to 2615. Now using the result which is given in the key idea we can find out the price index number. So the price index number p0 1 for the year 1985 written 80 as the base year is equal to summation of w into x over summation of w which is equal to 2615 33. Wait for a is 3 and wait for b is given that the value of index number 35 will change the weights applied to c and will have the given data. Then the wait for a is 3 and the wait for b is 2 and we have to find the wait for so we have drawn a table for the given data. Now here we have already calculated the value of x and p0 and p1 are also given to us. Now here for the second case it is given that the weights are changed that is the wait for a is 8 for v and the wait for c and the wait for 5 d v. At the total rate that is summation w is equal to now summation w is 15 that is on adding all the values of w we are getting that the wait for d that is z is equal to here we can write z is equal to 10 minus y. Now in the last column let us find w into x now here 225 into 3 is 675 then 200 into 2 is 400 into y is 150 by the whole 200 minus 150 y. Now on adding the different values of w into x here that is summation of w into x is equal to 2575 by 5. Now by the weighted average of price field to method the index number for the year 1885 taking 1980 as the base year summation of w into x whole upon summation w which is equal to 2575 plus 55 whole upon. Also here let the value of index number in 1985 which changed weights is 173 and 173 is equal to 2575 plus 55 whole upon. 2595 minus 2575 is equal to 5 y which implies 20 is equal to 55 and this gets y is equal to now we have taken the wait for c is y and the wait for d is 10 minus 4 c is equal to 1 of the given question and that's all for this session hope you all have enjoyed the session.