 Hello and welcome to the session. In this session we discuss the following question which says if x is to y is equal to 2 is to 3, find the ratio 3x plus 2y is to 9x plus 5y. Let's proceed with the solution now. We are given the ratio x is to y is equal to 2 is to 3. This means x upon y is equal to 2 upon 3. We need to find the ratio 3x plus 2y is to 9x plus 5y. Now this ratio can be written as 3x plus 2y upon 9x plus 5y. Now dividing the numerator denominator by y we get 3 into x upon y plus 2 upon 9 into x upon y plus 5. Now we will put the value of x upon y as 2 upon 3 so substituting x upon y equal to 2 upon 3 we get 3 into 2 upon 3 plus 2 upon 9 into 2 upon 3 plus 5. Now this 3 cancels with 3 and 3 3 times is 9 so this is equal to 2 plus 2 upon 3 multiplied by 2 is 6 plus 5. Thus we get this is equal to 4 upon 11 or you can say this is the ratio 4 is to 11. Thus we have the ratio 3x plus 2y is to 9x plus 5y is equal to 4 is to 11. So this is our final answer. This completes the session. Hope you have understood the solution for this question.