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

The correct option is B $5:1$

Let the third proportional to 12 and 30 be x.
Then, 12 : 30 :: 30 : x
$\iff$ 12x = 30 $\times$ 30
$\iff x=\frac{(30\times 30)}{12}=75$
$\therefore$ Third proportional to 12 and 30 = 75.
Mean proportional between 9 and $25=\sqrt{9\times 25}=15$
$\therefore$ Required ratio = 75 : 15 = 5 : 1.