Mean Proportional MCQ Quiz - Objective Question with Answer for Mean Proportional - Download Free PDF
Last updated on Jun 3, 2025
Latest Mean Proportional MCQ Objective Questions
Mean Proportional Question 1:
Find the mean proportional between 17 and 68.
Answer (Detailed Solution Below)
Mean Proportional Question 1 Detailed Solution
Given:
First number (a) = 17
Second number (b) = 68
Formula Used:
Mean Proportional = Square root of (a × b)
Calculation:
Product = 17 × 68 = 1156
Mean Proportional = Square root of 1156
Mean Proportional = √1156 = 34
Therefore, the mean proportional between 17 and 68 is 34.
Mean Proportional Question 2:
What will be the mean ratio of 0.25 and 0.64?
Answer (Detailed Solution Below)
Mean Proportional Question 2 Detailed Solution
Given:
Two numbers = 0.25 and 0.64
Formula used:
Mean ratio = √(a × b)
Calculation:
Mean ratio = √(0.25 × 0.64)
⇒ Mean ratio = √0.16
⇒ Mean ratio = 0.4
∴ The mean ratio of 0.25 and 0.64 is 0.4
Mean Proportional Question 3:
The mean proportional between 36 and 9 is:
Answer (Detailed Solution Below)
Mean Proportional Question 3 Detailed Solution
Given:
Number 1 = 36
Number 2 = 9
Formula Used:
Mean Proportional = √(Number 1 × Number 2)
Calculation:
Mean Proportional = √(36 × 9)
⇒ Mean Proportional = √324
⇒ Mean Proportional = 18
The mean proportional between 36 and 9 is 18.
Mean Proportional Question 4:
The mean proportion of \(\frac{a^2}{b^3}\)and \(\frac{9 b^2}{4 a^3}\) is _________.
Answer (Detailed Solution Below)
Mean Proportional Question 4 Detailed Solution
Given:
The mean proportion of \(\dfrac{a^2}{b^3}\) and \(\dfrac{9 b^2}{4 a^3}\).
Formula used:
Mean proportion between two values x and y = \(\sqrt{x \times y}\)
Calculations:
Let x = \(\dfrac{a^2}{b^3}\) and y = \(\dfrac{9 b^2}{4 a^3}\).
⇒ Mean proportion = \(\sqrt{\dfrac{a^2}{b^3} \times \dfrac{9 b^2}{4 a^3}}\)
⇒ Mean proportion = \(\sqrt{\dfrac{a^2 \times 9 b^2}{b^3 \times 4 a^3}}\)
⇒ Mean proportion = \(\sqrt{\dfrac{9 \times b^2 \times a^2}{4 \times b^3 \times a^3}}\)
⇒ Mean proportion = \(\sqrt{\dfrac{9}{4} \times \dfrac{b^2}{b^3} \times \dfrac{a^2}{a^3}} \)
⇒ Mean proportion = \(\sqrt{\dfrac{9}{4} \times \dfrac{1}{b} \times \dfrac{1}{a}} \)
⇒ Mean proportion = \(\sqrt{\dfrac{9}{4 \times a \times b}} \)
⇒ Mean proportion = \(\dfrac{\sqrt{9}}{\sqrt{4 \times a \times b}}\)
⇒ Mean proportion = \(\dfrac{3}{2 \sqrt{a b}}\)
∴ The correct answer is option (3).
Mean Proportional Question 5:
Two numbers are x and 4x, and their mean proportional is 456976. Find x.
Answer (Detailed Solution Below)
Mean Proportional Question 5 Detailed Solution
Given:
Two numbers are x and 4x, and their mean proportional is 456976.
Formula used:
If two numbers are a and b, their mean proportional is given by:
Mean Proportional = \(\sqrt{a \times b}\)
Calculation:
Mean Proportional = \(\sqrt{x \times 4x}\)
⇒ 456976 = \(\sqrt{x \times 4x}\)
⇒ 456976 = \(\sqrt{4x^2}\)
⇒ 456976 = 2x
⇒ x = \(\dfrac{456976}{2}\)
⇒ x = 228488
∴ The correct answer is option (4).
Top Mean Proportional MCQ Objective Questions
What is the sum of the mean proportional between 1.4 and 35 and the third proportional to 6 and 9?
Answer (Detailed Solution Below)
Mean Proportional Question 6 Detailed Solution
Download Solution PDFFormula used:
Mean proportion of a and b = √ab
Third proportion of a and b = b2/a
Calculation:
Mean proportions of 1.4 and 35
⇒ x = √(1.4 × 35)
⇒ x = √(49)
⇒ x = 7
Third proportion of 6 and 9
y = 92/6
⇒ y = 81/6
⇒ y = 13.5
Hence, the required sum = 7 + 13.5 = 20.5
∴ The correct answer is option (1).Find the mean proportional between 3 and 27.
Answer (Detailed Solution Below)
Mean Proportional Question 7 Detailed Solution
Download Solution PDFGiven:
a = 3, b = 27
Formula used:
Mean proportional = √(a × b)
Calculations:
⇒ Mean proportional = √(3 × 27)
⇒ Mean proportional = √(81)
⇒ Mean proportional = 9
Therefore, the mean proportional between 3 and 27 is 9.
The mean proportion between a number and 20 is 50. What is that number?
Answer (Detailed Solution Below)
Mean Proportional Question 8 Detailed Solution
Download Solution PDFGIVEN:
Mean proportional between a number and 20 = 50.
FORMULA USED:
Mean proportional to x, y is \( \sqrt( x\times y)\).
CALCULATION:
Let the required number be x
Now, the mean proportion is between x and 20 = 50.
⇒ \({\sqrt{ ( x \times 20 )}} \) = 50
⇒ x × 20 = 2500.
⇒ x = 125.
∴ The required number is 125.
When x is subtracted from each of 43, 38, 11 and 10, the numbers so obtained in this order, are in proportion. What is the mean proportional between (5x + 1) and (7x + 4)?
Answer (Detailed Solution Below)
Mean Proportional Question 9 Detailed Solution
Download Solution PDFGiven:
x is subtracted from, 43, 38, 11, and 10
Concept Used:
If a, b, c, and d are in proportion,
then a/b = c/d
If y is mean proportion of x, y, and z,
then y2 = x × z
Calculation:
⇒ (43 – x)/(38 – x) = (11 – x)/(10 – x)
⇒ (43 – x)(10 – x) = (38 – x)(11 – x)
⇒ 430 – 43x – 10x + x2 = 418 – 11x – 38x + x2
⇒ 430 – 53x = 418 – 49x
⇒ 430 – 418 = – 49x + 53x
⇒ 12 = 4x
⇒ x = 12/4
⇒ x = 3
The two numbers are,
5x + 1
⇒ 5(3) + 1
⇒ 16
7x + 4
⇒ 7(3) + 4
⇒ 25
Now mean proportion of 16 and 25,
⇒ √(16 × 25)
⇒ 4 × 5
⇒ 20
∴ The mean proportion of 5x+1 and 7x + 3 is 20.
If 12, x, 8 and 14 are in proportion, then what is the mean proportional between (x - 12) and (x + 4)?
Answer (Detailed Solution Below)
Mean Proportional Question 10 Detailed Solution
Download Solution PDFFormula:
Mean proportion of x and y = √xy
Calculation:
12, x, 8 and 14 are in proportion,
⇒ (12/x) = (8/14)
⇒ 8x = 14 × 12
⇒ x = 7 × 3 = 21
The mean proportional between (x - 12) and (x + 4) = √(21 - 12) × (21 + 4)
⇒ √9 × 25
⇒ 15
∴ The mean proportional is 15.
When P is subtracted from each of the numbers 8, 6, 2 and 9, the numbers so obtained in this order are in proportion. What is the mean proportional between (3P - 6) and (9P - 4)?
Answer (Detailed Solution Below)
Mean Proportional Question 11 Detailed Solution
Download Solution PDFGiven:
If P is subtracted from 8, 6, 2, and 9 then these numbers are in proportion.
Concept used:
If a, b, c and d are in proportion then
⇒ a/b = c/d
Mean proportion = √(a × b)
Calculation:
According to the question:
⇒ (8 - P)/(6 - P) = (2 - P)/(9 - P)
⇒ (8 - P) × (9 - P) = (2 - P) × (6 - P)
⇒ 72 - 8P - 9P + P2 = 12 - 2P - 6P + P2
⇒ 17P - 8P = 72 - 12
⇒ 9P = 60
⇒ P = 20/3
Mean proportion = √{(3P - 6) × (9P - 4)}
Now, Putting the value of P in the equation:
⇒ √{(3 × (20/3) - 6) × (9 × (20/3) - 4)}
⇒ √{(20 - 6) × (60 - 4)}
⇒ √{14 × 56}
⇒ 14 × 2 = 28
∴ The correct answer is 28.
If x is the mean proportional between 12.8 and 64.8 and y is the third proportional to 38.4 and 57.6, then 2x : y is equal to:
Answer (Detailed Solution Below)
Mean Proportional Question 12 Detailed Solution
Download Solution PDFIf x is the mean proportional between 12.8 and 64.8, then
12.8 : x : : x : 64.8
⇒ 12.8/x = x/64.8
⇒ x2 = 12.8 × 64.8
⇒ x = √[16 × 0.8 × 0.8 × 81]
⇒ x = 4 × 0.8 × 9
If y is the third proportional to 38.4 and 57.6, then
38.4 : 57.6 : : 57.6 : y
⇒ 38.4/57.6 = 57.6/y
⇒ y = (57.6 × 57.6)/38.4
⇒ y = 86.4
Now,
2x : y = 2 × 4 × 0.8 × 9 : 86.4 = 2 : 3
Short Trick :
Mean Proportional x = √12.8 × 64.8 = 28.8
Third proportional y = (57.6 × 57.6)/38.4 = 86.4
Now,
2x : y = 2 × 28.8 : 86.4 = 2 : 3The mean proportional of a and b is c. What the mean proportional of a2 c and b2 c?
Answer (Detailed Solution Below)
Mean Proportional Question 13 Detailed Solution
Download Solution PDFCalculations:
According to the question,
c² = ab
where c is the mean proportional of a and b
Now, the mean proportion of a²c and b²c
⇒ \(\bf \sqrt {b²c \times a²c} \)
⇒ a.b.c
⇒ c² × c
⇒ c³
Hence, The Required value is c³.
If 48, x2 and 27 are in proportion, then the value of x is:
Answer (Detailed Solution Below)
Mean Proportional Question 14 Detailed Solution
Download Solution PDFGiven:
48, x2 and 27 are in proportion
Concept:
Mean proportion of a, b and c is b2 = ac
Solution:
Mean proportion ⇒ (x2)2 = 48 × 27
⇒ x4 = 1296
⇒ x = 6
∴ The value of x is 6.
The mean proportion of 169 and 144 is:
Answer (Detailed Solution Below)
Mean Proportional Question 15 Detailed Solution
Download Solution PDFGiven:
The mean proportion of 169 and 144
Concept used:
If A : B :: C : D then (B × C) = (A × D)
Calculation:
Let the mean proportion be Q.
The proportion becomes = 169 : Q :: Q : 144
According to the concept,
(144 × 169) = (Q × Q)
⇒ Q2 = (144 × 169)
⇒ Q = 12 × 13
⇒ Q = 156
∴ The mean proportion of 169 and 144 is 156.