Mean Proportional MCQ Quiz - Objective Question with Answer for Mean Proportional - Download Free PDF

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.

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

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.

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).

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).

Formula 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

Given:

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.

GIVEN:

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.

Given:

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.   

Formula:

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. 

Given:

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, 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,

Given:

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.

Calculations:

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.

Given:

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.