The harmonic mean and geometric mean of two positive numbers are in the ratio $4 : 5$ , then two numbers are in the ratio

4 : 1

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

3 : 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2 : 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

5 :

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $4 : 1$
We know $G^{2} / A = H$
So $H / G = G / A$
$4 / 5 = G / A$
$4 / 5 = 2 \sqrt{a b} / (a + b)$
$4 a^{2} + 4 b^{2} + 8 a b = 25 a b$
$4 a^{2} - 17 a b + 4 b^{2} = 0$
$(4 a - b) (a - 4 b) = 0$
So the numbers are in the ratio $4 : 1$
Option A

Suggest Corrections

Similar questions

4 : 5

4 : 5.

4 : 5.

12 : 13

\frac{12}{13}

Join BYJU'S Learning Program