 Hello and welcome to the session. In this session we discussed the following question which says construct a composite index number from the following index numbers and weights. We are given the index numbers as 110, 80, 60, 90 and the respective weights as 5, 4, 3 and 2. Now consider n quantities x1, x2, x3 and so on, w1, w2, w3 and so on up to wn. The weighted average is equal to w1 plus x2, w2, x3, w3 plus and so on up to xn, wn and this is equal to summation xw upon summation w. This is the weighted arithmetic average. This is the key idea that we use for this question. Let's proceed with the solution now. In the question we are given the index numbers and the corresponding weights. So we can take these index numbers as the quantities. So we can say that x1 be equal to the first index number given which is 110, x2 be equal to the second index number given which is 80, then be equal to the third index number given which is 60, x4 be the fourth index number given to us which is 90. We are also given the respective weights which could be denoted by w1, w2, w3 and w4. So w1 that is the weight for the index number x1, then w2 that is the weight for the index number 80, then w3 that is the weight for the index number, 90 is we are supposed to construct a composite index number which would be same as the weighted arithmetic average. We can say that the composite index number is equal to x1, w1 plus x2, w2 plus x3, w3 plus x4, w4 and this here upon w1 plus w2 plus w3 plus w4. Now substituting the respective values we get this is equal to 110 into 50 into 4 plus 60 into 3 plus 90 into 2 and this here upon 5 plus 3 plus, so this is equal to 550 plus 320 plus 180 plus 180 and this here upon and this is equal to 1230 upon 14 then 2 7 times is 14 and 2 615 times is 1230 so 115 upon 7 is equal to 7.85, so thus the composite index number is equal to 87.85. The answer this completes the session but we have understood the solution of this question.