 Hello and welcome to the session. In this session we will discuss a question which says that the ratio of Alisha's weight to Kate's weight is 4.3 is to 11 by 6. If the weight of Kate is 66 kilograms, what is the sum of weights of Alisha and Kate? Now before starting the solution of this question we should know some results. And the first result is any friction of the form a upon b whole upon c upon d is equal to ad upon bc. Now if x upon y is equal to p upon q then we get x into q y that means if we have two ratios which are equal that is x over y is equal to p over q that means x into q is equal to y into p. Now these results will work out as a key idea for solving out the given question. And now we will start with the solution. Now in the question the ratio of Alisha's weight to Kate's weight is given as 4 by 3 is to 11 by 6 and the weight of Kate is also given as 66 kilograms and we have to find the sum of weights of Alisha and Kate in kilograms. Now given the ratio of Alisha's weight 11 by 6 that's given ratio. Now simply find the given ratio we get now and written as upon 3 whole upon 11 upon 6. The key idea we know that any friction of the form a upon b whole upon c upon g is equal to ad upon so here whole upon 3 into 11. Now of 3 x is 3 so dividing numerator denominator equation 1 by 3 into 6 upon 3 whole upon 3 into 11 upon 3. Now 3 into 2 is 6 and 3 into 1 is 3 which will be equal to 4 into 2 whole upon 1 into 11 which is equal to 11. Or you can write this ratio as now it is also given that Kate's weight is 66 kilograms. Now we have to find Alisha's weight so let Alisha's weight be x kilograms so the ratio of Alisha's weight to Kate's weight will be now for the key idea we know that if 2 ratios are equal then we can write them as i is equal to p upon q which means x into q is equal to p into y. Now this is the ratio of Alisha's weight to Kate's weight and this is also the ratio of Alisha's weight to Kate's weight. So we can write 8 is to 11 is equal to x is to 66 which implies 8 upon 11 is equal to x upon 60. Now I am corresponding into 66 is equal to x into 11 which implies 8 into 66 whole upon 11 is equal to f. Now the common fact 11 so dividing the numerator denominator the left hand side of equation 8 into 66 is 11 whole upon 11 upon 11 is equal to now 11 into 6 is 66 and 11 into 1 is 11 48 is equal to now Kate's weight is 66 is 48 kilograms so the sum of weights is equal to kilograms plus 66 kilograms 114 kilograms and which is our required answer so this is the solution of the given question and that's all for this session hope you all have enjoyed the session.