 Hello and welcome to the session. In this session we discussed the following question which says if 2x plus 5 is 2, 2x plus 9 is sub-duplicate ratio of 9 is to 25, find the value of x. Before we move on to the solution, let's see what is the sub-duplicate ratio. Now given a ratio a is to b, so the sub-duplicate ratio of the ratio a is to b is square root of a is to square root of b or a to the power 1 upon 2 is to b to the power 1 upon 2. This is the key idea that we use for this question. Let's proceed with the solution now. We are given that the ratio 2x plus 5 is to 2x plus 9 is the sub-duplicate ratio of the given ratio 9 is to 25. Now from the key idea we have that the sub-duplicate ratio of a is to b is square root of a is to square root of b. So using this key idea we get 2x plus 5 is to 2x plus 9 is equal to square root of 9 is to square root of 25 or this means 2x plus 5 upon 2x plus 9 is equal to square root of 9 upon square root of 25. Further we get 2x plus 5 upon 2x plus 9 is equal to 3 upon 5. Now cross multiplying we get 5 multiplied by 2x plus 5 the whole is equal to 3 multiplied by 2x plus 9 the whole. This gives us 10x plus 25 is equal to 6x plus 27. Now we need to find the value of x so for this we will transpose 6x to the left hand side and plus 25 to the right hand side. Thus we get 10x minus 6x is equal to 27 minus 25 that is we have 4x is equal to 2. To find the value of x we divide both sides by 4. 4 cancels with 4 and 2. 2 times is 4. So we get the value of x as 1 upon 2. So x equal to 1 upon 2 is our final answer. This completes the session hope you have understood the solution of this question.