 Hello and welcome to the session. In this session we discuss the following question which says find the duplicate ratios of the following ratios. First we have 8a is to 3b. In the second part we have x upon 2 is to y upon 3. First of all we see what is the duplicate ratio. Now duplicate ratio of the ratio a is to b is a square is to b square. That is when a is to b is compounded with itself we get the resulting ratio which is a square is to b square and this is the duplicate ratio. This is the key idea that we use in this question. Let's proceed with the solution now. In the first part we are given the ratio 8a is to 3b. We need to find the duplicate ratio of this ratio. Thus the required duplicate ratio is equal to 8a whole square is to 3b whole square. That is 64a square is to 9b square. Thus we say duplicate ratio of 8a is to 3b is equal to 64a square is to 9b square. So this is the final answer for the first part of the question. Now consider the second part in which we are given the ratio x upon 2 is to y upon 3. Let us now find out the duplicate ratio for this ratio. So the required duplicate ratio is equal to x upon 2 whole square is to y upon 3 whole square or you can say x square upon 4 is to y square upon 9. This can also be written as 9x square that is we cross multiply is to 4y square. So this is the required duplicate ratio that is duplicate ratio of x upon 2 is to y upon 3 is equal to 9x square is to 4y square. This is the answer for the second part of the question. This completes the session. Hope you have understood the solution of this question.