Question

find the numbers whose mean proportional is 24 and third proportional is 192.​

Answer 1

Answer:

24x = 192

x= 192/24

x = 8

answer

Answer 2

Answer:

Answer is 12 and 48

Step-by-step explanation:

Let the required number are X and Y.

As given, mean proportion of X and Y is 24.

$∴ \: \: \: \: 24 = \sqrt{x.y}$

$⟹ \: \: \: 24 \times 24 = xy \: \: \: ...(1)$

Now, let third proportion of X and Y is K, then

$x:y:k$

$\frac{x}{y} = \frac{y}{k}$

$⟹kx = {y}^{2}$

As given. K = 192

$∴ \: \: \: 192x = {y}^{2}$

$⟹x = \frac{ {y}^{2} }{192} \: \: \: \: ...(2)$

Putting the value of X in equation (1),

$x.y = 24 \times 24$

$⟹ \frac{ {y}^{2} }{192} .y = 24 \times 24$

$⟹ {y}^{3} = 24 \times 24 \times 192 \\ = 24 \times 24 \times 24 \times 8 \\∴ \: \: \: \: \: y = 24 \times 2 = 48$

Putting the value of Y is eqn. (2)

$x = \frac{ {(48)}^{2} }{192}$

$⟹ \frac{48 \times 48}{24 \times 8}$

$⟹2 \times 6 = 12$

Hence, the required number are 12 and 48.