If 125 : y :: y : 180, find the positive value of  y.

Correct option is A

Given:​

The proportion  125 : y :: y : 180

Formula Used:

For a proportion a : b :: b : c,

the middle term b is the geometric mean of  a and c :

​$$b = \sqrt{a \times c}$$​​

Solution: 

​$$\frac{125}{y} = \frac{y}{180}$$​​

​$$y^2 = 125 \times 180$$​​

​$$y^2 = 22,500$$​​

y = $$\sqrt{22,500}$$​​

y = 150