Find the ratio of mean proportional between 4 and 25 to third proportional to 8 and 20

A 1 : 5

B 2 : 5

C 5 : 1

D 1 : 3

E 2 : 7

Correct Answer: Option A

We know that,

Mean proportional between and b = √(a × b)

∴ Mean proportional between 4 and 25 = √(4 × 25) = √100 = 10.

We also know that,

Third proportional to a and b = b²/a

∴ Third proportional to 8 and 20 = (20)²/8 = 400/8 = 50

∴ Ratio of mean proportional between 4 and 25 to Third proportional to 8 and 20 = 10 : 50 = 1 : 5