Question
Download Solution PDFFind the third proportion of x and 30, when 45 : 12 : : 75 : x.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
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 = \(\frac{bc}{a}\)
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