What is the ratio of the third proportional of 0.4 and 0.8 to the mean proportional of 13.5 and 0.24?

8 : 9

Third proportional of a & b = \(\frac{b^2}{a}\)

Hence third proportional of .4 & .8 = \(\frac{(.8)^2}{.4}\) = 1.6

Mean proportional of a & b = \(\sqrt {ab}\)

Hence Mean proportional of 13.5 & .24 = \(\sqrt {13.5 × .24}\) = \(\sqrt {3.24}\) = 1.8

Required ratio ⇒ 1.6  :  1.8 ⇒ 8   :   9