If the mean proportional of 25 and 49 is x and the fourth proportional of 5, 8 and 15 is y. then the value of 5x - 7y is:

Correct option is C

Given:

The mean proportional of 25 and 49 is x

The fourth proportional of 5, 8, and 15 is y

Formula Used:

The mean proportional between two numbers a and b is given by:

​$$x = \sqrt{a \cdot b}$$​​

The fourth proportional of a, b, c is given by:

​$$y = \frac{b \cdot c}{a}$$​​

Solution:

​$$x = \sqrt{25 \cdot 49} = \sqrt{1225} = 35$$​​

​$$y = \frac{8 \cdot 15}{5} = \frac{120}{5} = 24$$​​

Now, 

​$$5x - 7y = 5 \times 35 - 7 \times 24 = 175 - 168 = 7$$​​