 Hello and welcome to this session. In this session we will discuss the question which says that an index of retail prices is the mean of 6 other price index numbers which are weighted as follows. Now here the weight for A is given as 308 for B that is given 85 and the weight for C is 60. The weight for D is 110, the weight for E is 95 and the weight for F is 350. The original index of retail prices are established at 100 if the final percentage increases in the various indices have occurred since that time and the index of retail prices now. Now here the percentage increase for A is 75 percent, for B it is 150 percent, for C it is 90 percent, for D it is 80 percent, for E it is 25 percent and for F it is 60 percent. Now before starting the solution of this question we should know a result and that is by weighted average of price-related method p1 is equal to summation of p1 over p0 into 100 the whole into w upon summation w which is further equal to summation of w into x over summation w where x is p1 over p0 into 100. That is x is the price-related which is equal to p1 over p0 into 100 where p1 denotes the current in prices and p1 denotes the lazy in prices of the given commodities under consideration and p1 is the price index number for the current year with reference to the price year and here w denotes the weights for the given commodities under consideration. Now this result will work out as a key idea for solving out the given question and now we will start with the solution. Now the question of weights for the different commodities are given to us and also it is given that the original index of retail prices are established at 100 and the percentage increases in the radius in the sales which have occurred since that time are also given to us. Now it is given that the weights in your prices for commodities A, B, C, D, P and F are of each and the price-related P which is equal to p1 over p0 into 100 are respectively 175, 190, 180, 125 and 160. Now the question is given that the percentage increase for A is 75 percent. Therefore the price related for A will be equal to 100 plus 75 percent of 100 which is 175 and it is also given that the percentage increase for B is 140 percent for the price related for B will be equal to 100 plus 140 percent of 100 which is equal to 230. And similarly we have got the price relatives of C, D, E and F. Now let us form a table for the given data that is for the weights of different commodities which are given to us. So using the price relatives and the weights which are given to us we will form a table. So we have drawn a table. In the first column we have written the commodities. In the second column we have written the corresponding weights of the different commodities. In the next column we have written the corresponding price relatives for the different commodities and in the last column we will find W into X. Well W are the weights for the different commodities denotes the price relatives for the different commodities. For the commodity A W into X will be equal to 900 for B it is 85 into 240 which is 20,400. For C it is 16 into 190 which is 11,400 for D, 110 into 180 is equal to 19,800 for E. It is 95 into 125 which is equal to 11,875. And for the commodity F W into X is equal to 56,000. Now on adding all the values of we are getting summation W is equal to 1008. The values of W into X we are getting summation of W into X is equal to 173,375. Now by using the result which is given in the key idea we can find out the price of X number. Therefore the required index is equal to summation of W into X over summation W. Now putting the values of summation of W into X and summation W this is equal to 173,375,171.999. Therefore the required index is 0.999 of the given question and that's all for this session. Hope you all have enjoyed this session.