 Hello and welcome to the session. In this session we discussed the following question which says which ratio is greater 5 is to 7 or 7 is to 9. Before moving on to the solution let's discuss the condition used to compare the two ratios. We are given two ratios A is to B and C is to D where B is not equal to 0 also D is not equal to 0. Then the ratio A is to B written as A upon B is greater than the ratio C is to D written as C upon D if and only if A D is greater than B C also A upon B would be equal to C upon D if and only if A D is equal to B C and A upon B would be less than C upon D if and only if A D is less than B C. This is the key idea that we use for this question. Let's move on to the solution now. We are given the two ratios 5 is to 7 and 7 is to 9. We have to check which one is greater out of the two given ratios. Now from here we have A as 5, B as 7 that is this ratio is taken as A is to B then if this ratio is taken as C is to D then C is 7 D is 9. Let us now find out A D and B C. Now A D would be equal to 5 multiplied by 9 that is 45 and B C would be equal to 7 multiplied by 7 which is 49. Now clearly 49 is greater than 45 that is B C is greater than A D or we can say that A D is less than B C. Now from the third condition of the comparison of ratios we find that A upon B is less than C upon D if and only if A D is less than B C. Now that we have got that A D is less than B C therefore we can say that A upon B is less than C upon D that is we have 5 upon 7 is less than 7 upon 9 or we can say the ratio 7 is to 9 is greater than the ratio 5 is to 7. Hence we can say that the ratio 7 is to 9 is greater than the ratio 5 is to 7. So this is our final answer. This completes the session. Hope you have understood the solution of this question.