The ratio between the third proportional of 12 and 30 and mean proportional of 9 and 25 is -

12 : 1
25 : 1
37 : 15
49 : 14

Answer:- 1

Explanation:-

Solution:

Let the third proportional to 12 and 30 be x.
Then,

\begin{aligned} = 12 : 30 :: 30 : x \\ \Rightarrow 12 x = 30 \times 30 \\ \Rightarrow x = \frac{(30 \times 30)}{12} = 75. \end{aligned}

$\eqalign{ & = 12:30::30:x \cr & \Rightarrow 12x = 30 \times 30 \cr & \Rightarrow x = \frac{{\left( {30 \times 30} \right)}}{{12}} = 75. \cr}$ ∴ Third proportional to 12 and 30 = 75
Mean proportional between 9 and 25

\begin{aligned} = \sqrt{9 \times 25} = 15. \\ ∴ Required ratio = 75 : 15 \\ = 5 : 1. \end{aligned}

$\eqalign{ & = \sqrt {9 \times 25} = 15. \cr & \therefore {\text{Required ratio}} = 75:15 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 5:1. \cr}$

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∴ Third proportional to 12 and 30 = 75
Mean proportional between 9 and 25

\begin{aligned} = \sqrt{9 \times 25} = 15. \\ ∴ Required ratio = 75 : 15 \\ = 5 : 1. \end{aligned}

$\eqalign{ & = \sqrt {9 \times 25} = 15. \cr & \therefore {\text{Required ratio}} = 75:15 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 5:1. \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

Let the third proportional to 12 and 30 be x.
Then,