Question

The ratio of third proportional to 12 and 30 and the mean proportional between
9 and 25 is:
(a) 2:1
(b) 5:1 (c)7:15 (d) 9:14​

Answer 1

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Plz Refer the pic !!

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Answer 2

$\huge \boxed{ \fcolorbox{cyan}{red}{Answer : }}$

$\bf{ \huge{ \underline{ \boxed{ \green{ \tt{5:1 \: }}}}}}$

option (b)

________________________________

$\bf \huge \underline{Question}$

The ratio of third proportional to 12 and 30 and the mean proportional between

9 and 25 is

1. 2:1
2. 5:1
3. 7:15
4. 9:14

___________________________________

$\bf \underline{step \: by \: step \: explanation}$

$\rm{let \: the \: 3rd \: proportional \: to \: 12 \: and \: 13 \: be \: x}$

$\sf{⟹then \: 12:30::30:x}$

$⟹ \sf{12x = 30 \times 30}$

$\sf{⟹x = \frac{30 \times 30}{12}}$

$\sf{⟹x = 75}$

so

$\rm{3rd \: proportional \: to \: 12 \: and \: 30 \: is \: 75}$

then now mean proportional between 9 and 25

$\sf{⟹ \sqrt{9 \times 25} = 15}$

required Ratio is = 75:15 = 5:1