What is the ratio of the mean proportional between 24 and 150 and the third proportional between 12 and $6\sqrt{5}$?

2 : 1 1 : 2 1 : 4 4 : 1

4 : 1

Mean Proportional = √24 x 150 = √3600 = 60. The third proportional x  12 : 6√5 :: 6√5 : x ⇒ 12x = 6√5 x 6√5 ⇒ 12x = 180  ⇒ x = 15, The required ratio = 60 : 15 = 4 : 1.