# The ratio of third proportional to 12 and 30 and the mean proportional between 9 and 25 is A) \[2:1\]B) \[5:1\]C) \[7:15\]D) \[9:14\]

Answer

Verified

234.5k+ views

**Hint:**In a continued proportion, the third proportional of two numbers \[a\] and \[b\] is defined to be that number \[c\] such that \[a:b = b:c\]. A mean proportional is a number that comes between two other numbers and which satisfies the equation \[\dfrac{a}{x} = \dfrac{x}{b}\].

**Complete step by step solution:**

Let the third proportional be \[x\],

So, the continued third proportion is \[12:30:x\]

i.e., \[12:30 = 30:x\]

\[\Rightarrow 12 \times x = 30 \times 30 \]

\[\Rightarrow x = \dfrac{{30 \times 30}}{{12}} \]

\[\Rightarrow x = \dfrac{{900}}{{12}} \]

\[\therefore x = 75 \]

Let the mean proportion be \[y\]. We know that a mean proportional is a number that comes between two other numbers and which satisfies the equation \[\dfrac{a}{x} = \dfrac{x}{b}\].

So, the mean proportion is \[\dfrac{9}{y} = \dfrac{y}{{25}}\]

\[\Rightarrow {y^2} = 9 \times 25\]

\[\Rightarrow {y^2} = 225 \]

\[\Rightarrow y = \sqrt {225} \]

\[\therefore y = 15 \]

Therefore, the ratio of third proportional to 12 and 30 and the mean proportional between 9 and 25 is \[x:y = 75:15 = 5:1\]

**Thus, the answer is option (B) \[5:1\]**

**Note:**A third proportional is also equal to the square of the second term, divided by the first term. And a mean proportional is equal to the square root of the product of first and second terms.

Last updated date: 28th May 2023

•

Total views: 234.5k

•

Views today: 1.91k

Recently Updated Pages

If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE