Find the third proportion of x and 30, when 45 : 12 : : 75 : x.

Given:

Find the third proportion of x and 30, when 45 : 12 : : 75 : x.

Formula used:

Third Proportional:

Let 'z' be the third proportional for a and b.

then, (a : b :: b : z)

Therefore, 

z = \(\frac{b^2}{a}\)

Calculation:

According to the question,

45 : 12 : : 75 : x.

It can be written as:

⇒ \(\frac{45}{12} = \frac{75}{x}\)

⇒ x = \(\frac{12 \times 75}{45}\) = 20

Now, 

Let y be the third proportional of 20 and 30.

⇒ y = \(\frac{30^2}{20}\)= 45

The third proportional of 20 and 30 = 45

Therefore, '45' is the required answer.

Additional Information

1. First Proportional:

Let 'x' be the first proportional for a, b and c.

then, (x : a :: b : c)

Therefore, 

x = \(\frac{ab}{c}\)

2. Mean Proportional:

Let 'x' be the mean proportional for a and b.

then, (a : x :: x : b)

Therefore, 

x = \(\sqrt{ab}\)

3. Fourth Proportional:

Let 'x' be the first proportional for a, b and c.

then, (a : b :: c : x)

Therefore, 

x = \(\frac{bc}{a}\)