 Hello and welcome to the session. In this session we will discuss a question which says that using simple average of price-related method, the price index for 1995, taking 1985 as base year was found to be 130, if summation p0 is equal to 435, find x and y from the following data. Now here the commodities are given as A, B, C, T and E and the corresponding prices in the year 1985 in dollars are given as 18, 95, x, 40 and 150 and the corresponding prices of the given commodities in the year 1995 in dollars are given as 95, 110, 85, y and 180. Now before starting the solution of this question we should know a result and that is by the simple average of price-related method, p0 1 is equal to summation of p1 over p0 into 100 the whole whole upon n where n is the number of items or commodities, p0 1 is the price index number for the current year with reference to the base year and p1 denotes the current year prices and p0 denotes the base year prices and even over p0 into 100 is the price relative. Now this result will work out as a key idea for solving out this question and now we will start with the solution. Now in the question using the simple average of price-related method the price index for the year 1995 taking 1985 as the base year is given as that is p1 1 is given as 130 and summation p1 is given as 435 this means the total of the basic prices of all the commodities under consideration is given as 435 and we have to find x and y that is we have to find x and y from the given data the prices in the year 1985 are the basic prices so adding all these prices we will get summation p0 which is also given to us as 435 so it is given summation p0 is equal to 435 from the given data summation p0 is equal to 80 plus 95 plus x plus 40 plus 150 now summation p0 is 435 is equal to 65 plus 8 minus 365 which is 70 now a table for the given data so we have drawn a table in the first column we have written the commodities in the second column the prices in the year 1985 in the third column we have written the prices in the year 1995 and we have made one more column in which we will calculate the price relatives now 1985 is the base year for the year 1995 so the base year prices are denoted by p0 the current year prices are denoted by p1 and the price related is equal to p1 over p0 in 200 and here we have written the value of x which we have got earlier that is x is equal to 70 we have to find the value of y this can create the price relatives for the different commodities now for the commodity a the price relative is p1 over p0 that is 95 over 80 into 100 which is equal to 118.75 for the commodity b price relative is equal to 110 over 95 into 100 which is equal to 115.79 for the commodity c the price relative is equal to 85 over 70 into 100 which is equal to 121.43 then for the commodity d the price relative is equal to y over 40 into 100 which is equal to 5 by 2 y for the commodity e the price relative is equal to 180 over 150 into 100 which is equal to 120 now adding all the values of the price relatives we are getting summation of p1 over p0 in 200 the whole is equal to 475.97 plus 5 by 2 into y now in the question the price index number p01 is given to us as 130 now using the research which is given in a key idea the average of the price relatives by using the arithmetic mean will give us the price index number that is the price index number p01 for the 1995 taking 1985 as the base year is equal to summation of p1 over p0 into 100 the whole whole upon n which is equal to now the number of commodities is 5 and also you have got the value of summation of p1 over p0 into 100 the whole so p1 over 1 will be equal to 475.97 plus 5 by 2 into y whole upon it is given that p01 is equal to 130 130 is equal to 475.97 plus 5 by 2 into y whole upon price that was multiplying 650 is equal to 475.97 plus 5 by 2 into y which further implies 5 by 2 into y is equal to 650 minus 475.97 which is equal to 174.03 which further implies y is equal to 174.03 into 2 whole upon 9.61 therefore y is equal to 69.61 we have got x is equal to 70 of the given question and that's all for this session hope you all have enjoyed this session.